COLLECTED  PAPERS  ON  ACOUSTICS 


WALLACE  CLEMENT  SABINE 


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ROBERT  D. 
fARHUHAR 

BOOKS  ON 
ARCHITECTURE 


I    NIVERSITY  OF  CALIFORNIA 
LOS  ANGELES 


COLLECTED  PAPERS 
ON  ACOUSTICS 


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COLLECTED  PAPERS 
ON  ACOUSTICS 


BY 

WALLACE   CLEMENT  SABINE 

LATE  HOLLIS  PROFESSOK  OF  MA  TIlKMATIf'S  AND  NATURAL  PHILOSOPHY 
IN  HAUVAItU  UNIVERSITY 


CAMBRIDGE 
ITARVARI)  INIVKHSITY  PRESS 

LONDON  :  111  Ml'IIKKV  MIl.lOliD 

OxFOni)  rsiVKItrtlTY   I'lttSS 


COPYRIGHT,  1922 
HARVARD  UNIVERSITY  PRESS 


Art 
Library 

PREFACE 

1  HIS  volume  aims  to  contain  all  the  important  contributions  to  the 
subject  of  acoustics  from  the  pen  of  the  late  Professor  W.  C  Sabine. 
The  greater  part  of  these  papers  appeared  in  a  number  of  different 
architectural  journals  and  were  therefore  addressed  to  a  changing 
audience,  little  acquainted  with  physical  science,  and  to  whose  mem- 
bers the  subject  was  altogether  novel.  Under  these  circumstances  a 
certain  amount  of  repetition  was  not  only  unavoidable,  but  desirable. 
Little  attempt  has  l)een  made  to  reiiuce  this  repetition  but  in  one 
case  an  omission  seemed  wise.  The  material  contained  in  the  author's 
earliest  papers  on  acoustics,  which  appeared  in  the  Proceedings  of 
the  American  Institute  of  Architects  in  1808,  is  repeated  almost 
completely  in  the  paper  which  forms  tiie  first  chapter  of  this  volume; 
it  has,  therefore,  been  omitted  from  this  collection  with  the  exception 
of  a  few  extracts  which  have  been  inserted  as  footnotes  in  the  first 
chapter. 

No  apology  is  made  for  the  preservation  of  the  paper  from  the 
Proceedings  of  the  Franklin  Institnic,  for,  tliough  nnieh  of  the  ma- 
terial therein  is  to  be  found  in  the  earlier  chapters  of  this  volume,  t  lie 
article  is  valuable  as  a  summary,  and  as  such  it  is  recommended 
to  the  reader  who  desires  to  obtain  a  general  view  of  the  subject. 

In  addition  to  the  papers  already  in  print  at  the  time  of  the 
author's  death  the  only  available  material  consisted  of  the  manu- 
scripts of  two  articles,  one  on  Echoes,  the  otiier  on  Whispering  Gal- 
leries, and  the  full  notes  on  four  of  the  lectures  on  acoustics  delivered 
at  the  Sorbonne  in  tiie  spring  of  1917.  Of  this  nuiterial,  the  first 
pa|X'r  was  discarded  as  being  too  fragmentary;  the  second,  after 
some  slight  omissions  juid  corrections  in  the  text  inade  necessary  by 
the  lo.ss  of  a  few  of  the  illustrations,  forms  Chapter  11  of  this  volume; 
an  al)slra<-l  of  so  nnicli  of  the  substance  of  the  lecture  notes  as  had 
not  alread\'  api)eared  in  print  has  i)i'eu  made,  of  which  j)art  is  to  be 
found  in  the  form  of  an  Ai)i)endix  ami  part  is  contained  in  some  of  the 
following  paragraphs. 

The  reader  may  often  be  j)uzzle(l  by  ref»'rence  to  works  about  to  be 
piililislied  l)ul  of  w  liicli  no  trace  is  to  be  found  in  I  Ills  \-oIuine.     It  is 


30oS';31 


vi  PREFACE 

u  nu'lanc'holy  fiut  that  tlu'se  papers  were  eitlier  never  written  or  else 
were  destroyed  l)y  their  author;  no  trace  of  them  can  he  found.  The 
extent  of  I  lie  labors  of  which  no  adequate  record  remains  may  best  be 
jutl^ed  from  the  following  extracts  taken  from  the  notes  on  the  Paris 
lectures  just  mentioned. 

"  On  the  one  hand  we  have  the  problem  (Reverberation)  which  we 
have  been  discussing  up  to  the  present  moment,  and  on  the  other 
the  whole  f|uestion  of  the  transmission  of  sound  from  one  room  to 
another,  through  the  walls,  the  doors,  the  ceiling  and  the  floors;  ami 
the  telei)honic  transmission,  if  I  may  so  call  it,  through  the  length  of 
the  structure.  It  is  five  years  ago  since  this  second  problem  was  first 
attacked  and  though  the  research  is  certainly  not  complete,  some 
groimd  has  been  covered.  A  quantitatively  exact  method  has  been 
established  and  the  transmission  of  sound  through  about  twenty 
different  kinds  of  partitions  has  been  determined. 

"  For  example:  Transmission  of  sound  through  four  kinds  of  doors 
has  been  studied;  two  of  oak.  two  of  pine,  one  of  each  kind  was 
paneled  and  was  relatively  thin  and  light;  one  of  each  kind  was  very 
heav^-,  nearly  four  centimetres  thick;  through  four  kinds  of  windows, 
one  of  plate  glass,  one  with  connnon  panes,  one  double  with  an  air 
space  of  two  centimetres  between,  one  with  small  panes  set  in  lead 
such  as  one  sees  in  churches;  through  brick  walls  with  plaster  on  both 
sides;  through  walls  of  tile  similarly  plastered;  through  walls  of  a 
character  not  common  in  France  and  which  we  call  gypsum  block; 
through  plaster  on  lath;  through  about  ten  different  kinds  of  sound 
insulators,  patented,  and  sold  in  quantities  representing  hundreds  of 
thousands  of  dollars  each  year,  yet  practically  without  value,  since 
one  can  easily  converse  through  six  thicknesses  of  these  substances 
and  talk  in  a  low  tone  through  three,  while  a  single  thickness  is  that 
ordinarily  (•inj)lo>-ed.  The  behavior  of  an  air  sjjace  has  been  studied, 
the  effect  of  tlie  thickness  of  this  air  space,  and  the  result  of  filling 
the  space  with  sand,  saw-dust  and  asbestos.  In  spite  of  all  this,  the 
research  is  far  from  complete  and  many  other  forms  of  construction 
nuist  be  investigated  before  it  will  be  possible  to  publish  the  results; 
these  determinations  must  be  made  with  the  greatest  exactness  as 
very  important  interests  are  involved.  .  .  . 


PREFACE  vii 

"  The  research  is  particuhirly  hiborious  because  resonance  has  a 
special  importance  in  a  great  number  of  forms  of  construction.  It  is  a 
much  greater  factor  in  transmission  than  in  absorption. 

"  I  sliall  not  enhirge  on  this  sul)ject  here  for  two  reasons:  first,  I 
believe  tliat  it  is  not  of  special  interest,  at  least,  in  its  present  state, 
and  second,  because  it  is  not  proj)er  to  present  a  formal  discussion  of 
this  subject  while  the  research  is  still  unfinished." 

The  last  i)aragrai)h  is  characteristic.  The  severity  of  tlie  criti- 
cism which  Professor  Sabine  always  applied  to  his  own  productions 
increased  with  time,  and  it  is  to  this  extreme  self-criticism  and  re- 
pression that  we  must  ascribe  the  loss  of  much  invaluable  scientific 
material. 

'J'hanks  are  due  to  The  American  Institute  of  Architects  and  to 
the  editors  of  The  American  Architect,  The  Brickbuilder,  The  En- 
gineering Record,  and  The  Journal  of  the  Franklin  Institute,  for 
permission  to  reprint  tlie  articles  which  originally  appeared  in  their 
respective  Journals. 

The  Editor  is  also  greatly  obliged  to  Dr.  Paul  Sabine  and  Mr.  Clif- 
ford M.  Swan  for  a  great  deal  of  valuable  material,  and  to  Mr.  Frank 
Chouteau  Brown  for  his  assistance  in  seeing  the  book  through  the 
press.  lie  is  ])articularly  indebted  to  his  colleague  Professor  F.  A. 
Saunders  for  his  invaluable  aid  in  all  matters  touching  the  correct 
presentation  of  the  material  of  this  volume. 

Theodore  LYiL\N 

JEFFERSON  PHYSICAL  L.XBOR.VTORV 

Hahvahi)  Univeksity 
Jniu-.  1!H1 


CONTENTS 

PAGE 

1.  Kcvcrbcration 3 

[The  American  Architect,  1900] 

2.  The  Accuracy  of  Musical  Taste  in  Regard  to  Architectural 

Acoustics.     The  Variation  in  Reverberation  with  Variation  in 

Pitch 69 

[Proceedings  of  the  American  Academy  of  Arts  and  Sciences,  Vol.  xui,  No.  2,  June, 
1900J 

3.  Melody  and  the  Origin  of  the  Musical  Scale 107 

[yice-Prexidenliat  Address,  Section  li,  American  Association  for  the  Adranecment 
of  Science,  Chicago,  1907] 

4.  Effects  of  Air  Currents  and  of  Temperature 117 

[Engineering  Record,  Juno,  1910] 

5.  Sense  of  Loudness 1-0 

[Contributions  from  the  Jefferson  Physical  Laboratory,  \'i>\.  \iii,  1910] 

6.  The  Correction  of  Acoustical  Difficulties        131 

[The  Arrhilecturul  Quarterly  of  Hanard  University,  March,  191i] 

7.  Theatre  Acoustics 163 

[The  American  Architect,  \o].  civ,  p.  257] 

8.  IJuilding  Material  and  Musical  Pilch      199 

The  liriekbuilder,  \(.l.  xxiii.  No.  1,  .laiuiary.  1914] 

9.  Architectural  Acoustics '■219 

[Journal  if  the  Franklin  Institute,  January,  1915] 

10.  Insulation  Sound 237 

|77i<  liriekbuilder.  Vol,  XXIV,  No.  2.  Fohniarv,  1915] 

11.  Whispering  fJallcries 255 

Ari'KNDix -77 

On  the  Mra.surcnicnt  of  tlic  Intensity  of  Sound  uiiilon  thoHoactionof  the  Uoom 
upon  the  Sound 


COLLECTED  PAPERS 
ON  ACOUSTICS 


REVERBERATION' 


INTRODUCTION 


1  HE  following  investigation  was  not  undertaken  at  first  by  choice, 
but  devolved  on  the  writer  in  1895  tlu-ough  instructions  from  the 
Corporation  of  Harvard  University  to  propose  changes  for  remedy- 
ing the  aoouslic-al  (!ifficulti(>.s  in  tlie  lecture-room  of  the  Fogg  Art 
Museum,  a  hiiiiding  tluil  luid  just  been  completed.  About  two  years 
were  sj)ent  in  exjierimenting  on  this  room,  and  permanent  changes 
were  then  nuide.  Almost  immediately  afterward  it  became  certain 
that  a  new  Boston  Music  Ilall  would  lie  erected,  and  the  questions 
arising  in  tiie  consideration  of  its  jilans  forced  a  not  unwelcome  con- 
tinuance of  the  general  investigation. 

No  one  can  appreciate  the  condition  of  architectural  acoustics  — 
the  science  of  sound  as  applied  to  buildings  —  who  has  not  with  a 
pressing  case  in  hand  souglit  tlirough  the  scattered  literature  for 
some  safe  guidance,  liespousibility  in  a  large  and  irretrievable  ex- 
jjenditure  of  money  compels  a  careful  consideration,  and  emphasizes 
the  meagerness  and  inconsistency  of  the  current  suggestions.  Thus 
the  most  definite  and  often  repeated  statements  are  such  as  the 
following,  that   the  dimensions  of  a  room  shoidd  be  in  the  ratio 

2  :  3  :  5,  or  according  to  some  writers,  1:1:2,  and  others,  2  :  3  :  4; 
it  is  probable  that  the  basis  of  these  suggestions  is  the  ratios  of  the 
harmonic  intervals  in  music,  but  the  connection  is  untraced  and  re- 
mote. Moreover,  such  .advice  is  rather  difficult  to  a])])ly;  shoidd  one 
measure  tlie  length  to  tlie  l)aek  or  lo  the  front  of  the  galleries,  to  the 
Itaek  or  tin-  front  of  the  stage  recess?  Few  rooms  have  a  flat  roof, 
where  should  the  height  Ix-  measured.^  One  writer,  wlio  Iiad  >eeu  llie 
Mormon  Temple.  reconuuencU'd  that  all  auditt)riums  l)e  elliptical. 
Sanders  Theatre  is  by  far  the  best  auililorium  in  Cambridge  and  is 
.semicircular  in  general  shape,  but  with  a  recess  that  nuikes  it  almost 
anxihing;   and,  on  I  lie  ol  her  hand,  I  he  leeture-rooni  in  the  Fogg  Art 

'  Tlu'  AiniTiian  .\rrliil(it  niiil  Tlic  Kiigioecring  Hccuril,  llXlii. 
5 


4  REM^RBERATION 

Miiseuin  is  also  scniicirciilar,  indeed  was  modeled  after  Sanders 
Tluatre,  and  it  was  the  worst.  But  Sanders  Theatre  is  in  wood  and 
flu-  Fofig  leclure-rooiii  is  plaster  on  tile;  one  seizes  on  this  only  to  be 
inunediatel}'  reniiiKled  that  Sayles  Ilall  in  Providence  is  largely 
lined  with  wood  and  is  bad.  Curiously  enough,  each  suggestion  is 
advanced  as  if  it  alone  were  sufficient.  As  examples  of  remedies, 
may  be  cited  the  placing  of  vases  al)Out  the  room  for  the  sake  of 
resonance,  wrongly  suj>posed  to  have  been  the  object  of  the  vases  in 
Greek  theatres,  and  the  stretching  of  wires,  even  now  a  frequent 
though  useless  device. 

The  problem  is  necessarily  complex,  and  each  room  presents  many 
conditions,  each  of  which  contributes  to  the  result  in  a  greater  or  less 
degree  according  to  circumstances.  To  take  justly  into  account  these 
varied  conditions,  the  solution  of  the  problem  should  be  quantitative, 
not  merely  qualitative;  and  to  reach  its  highest  usefulness  it  should 
be  such  (hat  its  application  can  precede,  not  follow,  the  construction 
of  the  building. 

In  order  that  hearing  may  be  good  in  any  auditorium,  it  is  neces- 
sary that  the  sound  should  be  sufficiently  loud ;  that  the  simultane- 
ous components  of  a  complex  sound  should  maintain  their  proper 
relative  intensities;  and  that  the  successive  sounds  in  rapidly  mov- 
ing articulation,  either  of  speech  or  music,  should  be  clear  and  dis- 
tinct, free  from  each  other  and  from  extraneous  noises.  These  three 
are  the  necessary,  as  they  are  the  entirely  sufficient,  conditions  for 
good  hearing.  The  architectural  problem  is,  correspondingly,  three- 
fold, and  in  this  introductory  paper  an  attempt  will  be  made  to 
sketch  and  define  briefly  the  subject  on  this  basis  of  classification. 
Within  the  three  fields  thus  defined  is  comprised  without  exception 
the  whole  of  architectural  acoustics. 

1.  Loudness.  —  Starting  with  the  simplest  conceivable  auditorium 
—  a  level  and  open  plain,  with  the  ground  bare  and  hard,  a  single 
person  for  an  audience  —  it  is  clear  that  the  sound  spreads  in  a  hemi- 
spherical wave  diminishing  in  intensity  as  it  increases  in  size,  pro- 
portionally. If,  instead  of  being  hare,  the  ground  is  occupied  by  a 
large  audience,  the  sound  diminishes  in  intensity  even  more  rapidly, 
being  now  absorbed.  The  upper  part  of  the  sound-wave  escapes  un- 
affected, but  the  lower  edge  —  the  only  part  that  is  of  service  to  an 


INTRODUCTION  5 

audience  on  a  plain  —  is  rapidly  lost.  The  first  and  most  obvious 
improvement  is  to  raise  the  speaker  above  the  level  of  the  audience; 
the  second  is  to  raise  the  seats  at  the  rear;  and  the  third  is  to  place  a 
wall  behind  the  speaker.  Tlie  result  is  most  attractively  illustrated 
in  the  Greek  theatre.  These  changes  being  made,  still  all  the  sound 
rising  at  any  consideriiblc  ;iiigle  is  lost  through  the  opening  above, 
and  onl.\'  pari  of  the  speaker's  efforts  serve  the  audience.  When  to 
this  auditorium  a  roof  is  added  the  average  intensity  of  sound 
throughout  the  room  is  greatly  increased,  especially  that  of  sustained 
tones;  and  the  intensity  of  sound  at  the  front  and  the  rear  is  more 
nearly  ecpialized.  If,  in  addition,  galleries  be  constructed  in  order  to 
elevate  the  distant  part  of  the  audience  and  bring  it  nearer  to  the 
front,  we  Iiavc  the  gcncriil  lorin  of  the  modern  auditorium.  The 
problem  of  calculating  the  loudness  at  different  parts  of  such  an  audi- 
torium is.  obviously,  com])I('X,  but  it  is  perfectly  determinate,  and  as 
soon  as  the  rcHecting  and  absorbing  power  of  the  audience  and  of  the 
various  wall-surfaces  are  known  it  can  be  solved  approximately. 
Under  this  head  will  l)e  considered  the  effect  of  sounding-boards,  I  lie 
relative  merits  of  different  materials  used  as  reflectors,  the  refrac- 
tion of  sound,  and  the  influence  of  the  variable  temperature  of 
the  air  through  the  heating  antl  ventilating  of  the  room,  and  similar 
subjects. 

'2.  DiatortioH  of  Complex  Sounds:  Inierference  and  Resonance.  — 
In  discussing  the  subject  of  loudni'ss  the  direct  and  reflected  sounds 
have  bei'U  spoken  of  as  if  always  reenforcing  each  other  when  tiiey 
come  together.  A  moment's  consideration  of  the  nature  of  sound 
will  >\\n\\  (hat.  as  a  mallei'  of  I'acl,  it  is  entirely  possible  for  tlieiu  to 
o|)l)osi'  each  other,  'i'he  sounding  l)0(iy  in  its  forward  motion  sends 
off  a  wave  of  condensation,  which  is  immediately  followed  through 
the  air  1)\-  a  wave  of  rarefaction  produced  l)y  the  vil)rating  body  as 
it  ni()\es  l)a(k.  'i'hese  two  \\;L\-es  of  opposite  character  taken  to- 
gether constitute  u  sound-wave.  The  source  continuing  to  vibrate, 
these  waves  follow  each  other  in  a  train.  Hearing  in  nn'nd  this  alter- 
nating character  of  sound,  it  is  evident  that  should  the  sound  travel- 
ing by  different  palll^  by  reflection  from  different  walls- — come 
together  again,  I  he  palli>  luing  e(|ual  in  lenglli,  condensation  will 
arrive  at  the  >anie  time  as  eoiHJensal  ion,  and  reenforce  it.  and  rare- 


(I  HK\KUBKRATION 

faction  will,  .similarly,  rt'onforcc  rarefaction.  But  should  one  path 
be  a  little  shorter  Hum  tlu-  otiur,  rarcfaclion  i)y  one  and  condensa- 
tion l)y  tlic  otluT  may  arrive  at  the  same  time,  and  at  this  point 
IIhtc  will  l)e  comparative  .silence.  The  whole  room  may  be  mapped 
out  into  regions  in  which  the  sound  is  loud  and  regions  in  which  it 
is  ftH'ble.  When  there  are  many  reflecting  surfaces  the  interference 
is  imicli  more  compU'X.  When  the  note  changes  in  pitch  the  inter- 
ference .system  is  entirely  altered  in  character.  A  single  incident 
will  serve  to  illustrate  this  point.  There  is  a  room  in  the  Jefferson 
Physical  Lal)oratory,  known  us  the  constant-temperature  room, 
that  has  been  of  the  utmost  service  throughout  these  experiments. 
It  is  in  the  center  of  one  wing  of  the  building,  is  entirely  under 
ground,  even  below  the  level  of  the  l)asenient  of  the  building,  has 
separate  loinulations  and  (loui)le  walls,  each  wall  being  very  thick 
and  of  brick  in  cement.  It  was  originally  designed  for  investiga- 
tions in  heat  requiring  constant  temperature,  and  its  peculiar  loca- 
tion and  construction  were  for  this  ])urpose.  As  it  was  not  so  in 
use,  however,  it  was  turned  over  to  these  experunents  in  sound,  and 
a  room  more  suitable  could  not  be  designed.  From  its  location  and 
construction  it  is  extremely  quiet.  Without  windows,  its  walls, 
floor,  and  ceiling  —  all  of  solid  masonry  —  are  smooth  and  un- 
liroken.  The  single  door  to  the  room  is  plain  and  flush  with  the 
wall.  The  dimensions  of  the  room  are,  on  the  floor,  i.'il  X  6.10 
meters;  its  heiglit  at  the  walls  is  2.54  meters,  but  the  ceiling  is 
slightly  arched,  giving  a  height  at  the  center  of  3.17  meters.  This 
room  is  here  described  at  length  because  it  will  be  frequently  re- 
ferred to,  particularly  in  this  matter  of  interference  of  sound.  While 
working  in  this  room  with  a  treble  c  gemshorn  organ  pipe  blown  by 
a  steady  wind-pressure,  it  wsis  observed  that  the  pitch  of  the  pipe 
api)arently  changed  an  octave  when  the  observer  straightened  up 
in  his  chair  from  a  position  in  which  he  was  leaning  forward.  The 
exi)lanation  is  this:  The  organ  pipe  did  not  give  a  single  pure  note, 
but  gave  a  fundamental  treble  c  accompanied  by  several  overtones, 
of  which  the  strongest  was  in  this  case  the  octave  above.  Each  note 
in  the  whole  complex  sound  had  its  own  interference  system,  which, 
as  long  as  the  sound  remained  constant,  remained  fixed  in  position. 
It  so  happened  that  at  these  two  points  the  region  of  silence  for  one 


INTRODT'CTIOX  7 

note  coincided  with  the  region  of  reenforcement  in  tlie  other,  and 
vice  versa.  Thus  the  observer  in  one  position  heard  the  fundamental 
note,  and  in  the  other,  the  first  overtone.  The  change  was  exceed- 
ingly striking,  and  as  the  notes  remained  constant,  the  experiment 
could  be  trietl  again  and  again.  With  a  little  search  it  was  possible 
to  find  other  points  in  the  room  a  I  wliicli  the  same  phenomenon 
appeared,  but  generally  in  less  pertVclion.  'I"he  distortion  of  the 
relative  intensities  of  the  components  of  a  chord  that  may  thus  be 
protluced  is  evident.  Practically  almost  every  sound  of  the  voice 
in  speech  and  song,  and  of  instrumental  music,  even  single-part 
music  so-called,  is  more  or  less  complex,  and.  therefore,  subject  to 
this  distortion.  It  will  be  necessary,  later,  to  show  under  what  cir- 
cumstances this  phenomenon  is  a  formidable  danger,  and  how  it 
may  be  guarded  against,  and  under  what  circumstances  it  is  negli- 
gible. It  is  evident  from  the  above  occurrence  that  it  may  be  a  most 
serious  matter,  for  in  this  room  two  persons  side  by  side  can  talk 
together  with  but  little  comfort,  most  of  the  difficulty  being  caused 
by  the  interference  of  sound. 

There  is  another  phenomenon,  in  its  occurrence  allied  to  inter- 
ference, liul  in  nature  distinct  —  the  phenomenon  of  resonance. 
Both,  however,  occasion  the  same  evil  —  the  distortion  of  that  nice 
adjustment  of  the  relative  intensities  of  the  components  of  the 
conii)lex  sounds  that  constitute  speecii  and  nuisic.  The  phenome- 
non of  interference  just  discussed  merely  alters  the  distribution  of 
sound  in  the  room,  causing  the  intensity  of  any  one  pure  sustained 
note  to  be  above  or  below  the  average  intensity  at  near  points. 
Resonance,  on  the  other  hand,  alters  the  total  amount  of  sound  in 
the  whole  room  and  always  increases  it.  This  phenomenon  is 
noticeable  at  times  in  using  the  voice  in  a  small  room,  or  even  in 
particular  locations  in  a  large  room.  Perhaps  its  occurrence  is  most 
easily  obsc-rved  in  setting  up  a  large  church  organ,  where  the  pipes 
nuist  be  readjusted  for  tlie  i)arli(ular  s])ace  in  wiu'cii  the  organ  is  to 
stand,  iKi  iiiallcr  willi  liow  iiiurli  care  the  organ  may  lia\c  been 
assemijled  ami  ;i(ljii>i(il  lid'oic  lc.i\ing  the  factory.  The  general 
I)heii()nienon  of  resouaMce  is  of  very  wide  occurn-nce,  not  nu-rely  in 
acoustics  l)ut  in  mori-  gross  meciuinics  as  well,  as  the  vibration  of  a 
bridge  to  a  properly  timed  tread,  or  the  excessive  rolling  of  a  boat 


8  RE^TRBERATION 

in  certain  scjus.  The  principlf  is  tlio  same  in  all  eases.  I'lie  follow- 
ing conception  is  an  easy  one  to  gnusp,  and  is  closelj-  analogous  to 
acoustical  resonance:  If  the  palm  of  the  hand  be  placed  on  the 
center  of  the  surface  of  water  in  a  large  basin  or  tank  and  quickly 
depressed  and  raised  once  it  will  cause  a  wave  to  spread,  which, 
reflected  at  the  edge  of  the  water,  will  return,  in  part  at  least,  to 
the  hand.  If,  just  as  the  wave  reaches  the  hand,  the  hand  repeats 
its  motion  with  the  same  force,  it  will  reenforce  the  wave  traveling 
over  the  water.  Thus  reenforced,  the  wave  goes  out  stronger  than 
before  and  returns  again.  By  continued  repetition  of  the  motion 
of  the  hand  so  timed  as  to  reenforce  the  wave  as  it  returns,  the  wave 
gets  to  be  very  strong.  Instead  of  restraining  the  hand  each  time 
until  the  wave  traveling  to  and  fro  returns  to  it,  one  may  so  time 
the  motion  of  the  hand  as  to  have  several  equal  waves  following 
each  other  over  the  water,  and  the  hand  each  time  reenforcing  the 
wave  that  is  passing.  This,  obviously,  can  be  done  by  dividing  the 
interval  of  time  between  the  successive  motions  of  the  hand  by  any 
whole  mmiber  whatever,  and  moving  the  hand  with  the  frequency 
thus  defined.  The  result  will  be  a  strong  reenforcement  of  the  waves. 
If,  however,  the  motions  of  the  hand  be  not  so  timed,  it  is  obvious 
that  the  reenforcement  will  not  be  perfect,  and,  in  fact,  it  is  possible 
to  so  time  it  as  exactly  to  oppose  the  returning  waves.  The  appli- 
cation of  this  reasoning  to  the  phenomenon  of  sound,  where  the  air 
takes  the  place  of  the  water  and  the  sounding  body  that  of  the  hand, 
needs  little  additional  explanation.  Some  notes  of  a  complex  sound 
are  reenforced,  some  are  not,  and  thus  the  quality  is  altered.  This 
phenomenon  enters  in  two  forms  in  the  architectural  problem:  there 
may  be  either  resonance  of  the  air  in  the  room  or  resonance  of  the 
walls,  and  the  two  cases  must  receive  separate  discussion;  their 
effects  are  totally  different. 

The  word  "resonance"  has  been  used  loosely  as  synonj-mous 
with  "reverl)eration,"  and  even  with  "echo,"  and  is  so  given  in 
some  of  the  more  voluminous  but  less  exact  popular  dictionaries. 
In  scientific  literature  the  term  has  received  a  very  definite  and 
precise  application  to  the  phenomenon,  wherever  it  may  occur,  of 
the  growth  of  a  vibratory  motion  of  an  elastic  body  under  periodic 
forces  timed  to  its  natural  rates  of  vibration.     A  word  having  this 


IXTRODTCTION  9 

significance  is  necessary;  and  it  is  very  desirable  that  the  term 
should  not,  even  popularly,  by  meaning  many  things,  cease  to  mean 
anything  exactly. 

3.  Confusion:  Reverberation,  Echo  and  Extraneous  Sounds.  — 
Sound,  being  energy,  once  produced  in  a  confined  space,  will  con- 
tinue until  it  is  cither  transmitted  by  the  boundary  walls,  or  is 
transformed  into  some  other  kind  of  energj',  generally  heat.  This 
process  of  decay  is  called  absorption.  Thus,  in  the  lecture-room  of 
Harvard  University,  in  which,  and  in  ])ehalf  of  which,  this  investi- 
gation was  begun,  the  rate  of  absorption  was  so  small  that  a  word 
spoken  in  an  ordinary  tone  of  voice  was  audible  for  five  and  a  half 
seconds  afterwards.  During  this  time  even  a  very  deliberate 
speaker  would  have  uttered  the  twelve  or  fifteen  succeeding  sylla- 
bles. Thus  the  successive  enunciations  blended  into  a  loud  sound, 
through  which  and  above  which  it  was  necessary  to  hear  and  dis- 
tinguish the  ortlerly  progression  of  the  speech.  Across  the  room 
this  could  not  be  done;  even  near  the  speaker  it  could  be  done  onlj' 
with  an  effort  wearisome  in  the  extreme  if  long  maintained.  With 
an  audience  filling  the  room  the  conditions  were  not  so  bad,  but 
still  not  tolerable.  This  may  be  regarded,  if  one  so  chooses,  as  a 
process  of  multiple  reflection  from  walls,  from  ceiling  and  from  floor, 
first  from  one  and  then  another,  losing  a  little  at  each  reflection 
imtil  ultimately  inaudible.  This  jihcnoiuenon  will  be  called  re- 
verlxTation,  including  as  a  special  case  the  echo.  It  must  be  ob- 
served, however,  that,  in  general,  reverberation  results  in  a  mass  of 
sound  filling  the  whole  room  and  incapable  of  analysis  into  its  dis- 
tinct reflections.  It  is  thus  more  difficidt  to  recogiu'ze  and  im])()ssible 
to  locate.  The  term  echo  will  Ije  res«'rved  for  that  particular  case 
in  which  a  short,  sharp  soimd  is  distinctly  repeated  by  reflection, 
either  once  from  a  single  surface,  or  several  times  from  two  or  more 
surfaces.  In  the  general  case  of  reverberation  we  are  only  concerned 
with  the  rate  of  decay  of  the  sound.  In  the  s])eeial  case  of  the  echo 
we  are  concerned  not  merely  with  its  intt-nsity.  Init  with  the  interval 
of  time  elapsing  between  the  initial  .sound  and  the  moment  it 
reaches  the  observer.  In  the  room  mentioned  as  the  occasion  of 
this  investigation,  no  discrete  echo  was  distinctly-  ])ere«'])til)le,  and 
the  case  will  serve  exci-llently  as  an  illustration  of  tiie  more  general 


10  RK\T-RBERATIOX 

tyiM-  of  rcvcrlM-ratioii.  AfUr  proliininary  gropings,'  first  in  the 
lih-riitiirf  anil  llu'ii  witli  st-Vi-ial  optical  di-vicrs  for  iiu-asiiring  tiu- 
intensity  of  sound,  both  were  al>an(loiu'(l,  llit'  latter  for  reasons  that 
will  1m-  e\|)laineil  later.  Instead,  the  rate  of  decay  was  measured  by 
nieiLsnring  what  was  inversely  proportional  to  it  — the  duration  of 
audibility  of  the  reverberation,  or,  as  it  will  be  called  here,  the  dura- 
tion of  andiliilily  of  the  residual  sound.  These  experiments  may  be 
I'xplained  to  advantage  even  in  this  introductory  paper,  for  they 
will  give  more  clearly  than  would  abstract  discussion  an  idea  of  the 
nature  of  reverberation.  Hioadly  considered,  there  are  two,  and 
only  two,  variables  in  a  room  shape  including  size,  and  materials 
including  furnishings.  In  designing  an  auditorium  an  architect  can 
give  consideration  to  both;  in  repair  work  for  bad  acoustical  con- 
ditions it  is  generally  impracticable  to  change  the  shape,  and  only 
variations  in  materials  and  furnishings  are  allowable.  This  was, 
therefore,  the  line  of  work  in  this  case.  It  was  evident  that,  other 
t lungs  being  ec|ual,  the  rate  at  which  the  reverberation  would  dis- 
ai)pt'ar  was  proportional  to  the  rate  at  which  the  sound  was  ab- 
sorl)e<l.  The  first  work,  therefore,  was  to  determine  the  relative 
absorbing  ])ower  of  various  substances.  With  an  organ  l)ipe  as  a 
constant  source  of  sound,  and  a  suitable  chronograph  for  recording, 
the  duration  of  audibility  of  a  sound  after  the  .source  had  ceased  in 
this  room  when  emjjty  was  found  to  be  5.62  seconds.  All  the  cush- 
ions from  the  seats  in  Sanders  Theatre  were  then  brought  over  and 
stored  in  the  lobby.  On  bringing  into  the  lecture-room  a  number 
of  cushions  having  a  total  length  of  8.2  meters,  the  duration  of 
audibility  fell  to  5. .'53  seconds.  On  bringing  in  17  meters  the  sound 
in  the  room  after  the  organ  pipe  ceased  was  audible  for  but   4.94 

'  TIh'  first  nirtliixl  fordolcrmining  tlieraloof  dec-ay  of  the  sdiiiuI.  ami  therefore  theamoiiiit 
of  nl>!u>riiliiin.  was  by  means  of  a  sensitive  nianometric  gas  flame  measured  by  a  miorometer 
toles<ii|M\  Ijiter.  photngraphinK  the  flame  was  tried;  but  both  method.s  were  abandoned,  for 
lliey  both  showed,  what  the  unaiiled  ear  eoulil  |)erceivc,  that  the  suund  as  observed  at  any 
p<iint  in  the  room  died  away  in  a  fluetuating  manner,  passing  through  maxima  and  minima. 
Moroiver,  they  showed  wlial  the  unaided  ear  had  not  deteetefl.  but  immediately  afterward 
did  rccogniw,  that  the  sound  was  often  more  intense  immediately  after  the  source  ceased  than 
tiefore.  .\ll  this  was  interesting,  but  it  rendered  impossible  any  accurate  interpretation  of  the 
results  obtaine<l  by  these  or  similar  methods.  It  was  then  found  that  the  ear  itself  aided  by 
n  suitable  elerlrical  i'hn>nograph  for  recording  the  duration  or  audibility  of  the  residual  sound 
gave  a  suriirisingly  sensitive  and  accurate  method  of  measurement.  Proe.  .\merican  Institute 
of  .\rehilecl.s,  p.  .15.  1898. 


INTRODUCTION  11 

seconds.  Evidently,  the  cushions  were  strong  absorbents  and 
raj)i(lly  ini[)r()viiif;  tlie  room,  at  least  to  the  extent  of  (liniiiiishiiiff  the 
reverberation.  The  result  was  interesting  and  the  process  was  con- 
tinued. Little  by  little  the  cushions  were  brought  into  the  room, 
and  each  time  the  duration  of  audibility  was  measured.  When  all 
the  seats  (43G  in  number)  were  covered,  the  sound  was  audible  for 
2.03  seconds.  Then  the  aisles  were  covered,  and  then  the  j)latf()rin. 
Still  there  were  more  cushions  -  -  almost  half  as  many  more.  'J'hese 
were  brought  into  the  room,  a  few  at  a  time,  as  before,  and  (haped 
on  a  scaffolding  (hat  had  been  erected  around  the  room,  the  tlura- 
tion  of  the  soimd  being  recorded  e;ich  lime.  Finally,  when  all  the 
cushions  from  a  theatre  seating  nearly  fifteen  lumdred  persons  were 
placed  in  the  room  —  covering  the  seats,  the  aisles,  the  platform, 
the  rear  wall  to  llic  ceiling  —  the  duration  of  audibility  of  the  resid- 
ual sound  was  1.1-t  seconds.  This  experiment,  recjuiring,  of  course, 
several  nights'  work,  having  been  completed,  ail  the  cushions  were 
removed  ami  the  room  was  in  n-adiness  for  the  test  of  other  absorb- 
ents. It  was  evident  that  a  standard  of  comparison  liad  i)een 
established.  Curtains  of  chenille,  1.1  meters  wide  and  17  meters  in 
total  length,  were  draped  in  the  room.  The  duration  of  audibility 
was  then  l.al  seconds.  Turning  to  the  data  that  had  just  been 
collected  it  appeared  that  this  amount  of  chenille  was  equivalent  to 
30  meters  of  Sanders  Theatre  cushions.  Oriental  rugs,  Herez, 
Deniirjik,  and  Hindoostanee,  were  tested  in  a  similar  manner;  as 
were  also  cretonne  cloth,  canvas,  and  hair  felt.  Similar  experi- 
ments, but  in  a  smaller  room,  determined  the  absorbing  power  of 
a  man  and  of  a  woman,  always  by  determining  the  number  of  run- 
ning meters  of  Sanders  Theatre  cushions  Dial  would  produce  tlie 
same  efTecl.  This  ])r()cess  of  c()mi)aring  two  alisorbents  by  actually 
substituting  one  for  the  other  is  laborious,  and  it  is  given  here  only 
to  show  the  first  steps  in  the  development  of  a  method  that  will  be 
expanded  in  the  following  papers. 

In  this  lecture-room  felt  wius  finally  placed  permanently  on  i)ar- 
ticular  walls,  and  the  room  was  rendered  not  excellent,  but  entirely 
serviceable,  and  it  has  been  used  U)v  the  pa>l  tiu-ee  yi-ars  without 
serious  complaint .  It  i^  not  inltiidcd  to  discuss  this  particular  case 
in  the  introductory  paper.  becau,se  such  discu.ssion  would  i>e  prema- 


li  R?:\TRBKRATK)\ 

tun-  aiul  logically  inconipK-ti'.  It  is  mentioned  here  iiierely  to  illus- 
trate concretely  the  subject  of  reverberation,  and  its  dependence  on 
absorpti*>n.  It  would  be  a  niislake  to  suppose  tliat  an  absorbent  is 
ulwavs  desirable,  or  even  when  desirable  that  its  position  is  a  matter 
of  no  consequence.' 

While  the  logical  order  of  considering  the  conditions  contributing 
to  or  interfering  with  distinct  hearing  would  be  that  enijjloyed  above, 
it  so  hai)pens  that  exactly  the  reverse  order  is  jjreferable  frcmi  an 
exi)erinienlal  standpoint.  By  taking  up  the  subject  of  reverberation 
first  it  is  possible  to  determine  the  coefficients  of  absorption  and 
reflwtion  of  various  kinds  of  wall  surface,  of  furniture  and  draperies, 
and  of  an  audience.  The  investigation  of  reverberation  is  now,  after 
five  years  of  exi)erimental  work,  comj>leted,  and  an  account  will  be 
rendered  in  the  following  papers.  Some  data  have  also  been  secured 
on  the  other  to|)ics  and  will  be  published  as  soon  as  rounded  info 
definite  form. 

This  paper  may  Ik-  n-garded  ius  introductory  to  the  general  sub- 
ject of  architectural  acoustics,  and  immediately  introductory  to  a 
series  of  articles  dealing  with  tlie  subject  of  reverberation,  in  which 
the  general  line  of  procedure  will  be,  briefly,  as  follows:  The  absorb- 
ing power  of  wall-surfaces  will  be  determined,  and  the  law  according 
to  which  the  reverberation  of  a  room  depends  on  its  volume  will  be 
demonstrated.  The  absolute  rate  of  decay  of  the  residual  sound  in 
a  number  of  rooms,  and  in  the  same  room  under  different  conditions, 
will  then  be  determined.    In  the  fifth  paper  a  more  exact  analysis 

'  Tlicrc  is  no  simple  Irc.itment  tlial  ciiii  cure  all  cases.  There  may  be  ina<lequate  absorption 
anil  prolonged  residual  sound;  in  this  case  absorbing  material  should  be  added  in  the  proper 
places.  On  the  other  hand,  there  may  be  excessive  absorption  by  the  nearer  parts  of  the  hall 
and  by  the  nearer  audience  and  the  sound  may  not  penetrate  to  the  greater  distances.  Ob- 
viously the  treatment  should  not  be  the  same.  There  is  such  a  room  belonging  to  the  Uni- 
versity, known  hx-ally  as  Sever  35.  It  is  low  and  long,  .\cross  its  ceiling  are  now  stretched 
huniire<is  of  w  ires  and  many  yards  of  cloth.  The  former  has  the  merit  of  being  harmless,  the 
latter  is  like  bleeiling  a  patient  suffering  from  a  chill.  In  general,  should  the  sound  seem 
smothered  or  loo  faint,  it  is  because  the  sound  is  either  imperfectly  distributed  to  the  audience, 
or  is  tost  in  waste  places.  The  first  may  occur  in  a  very  low  and  long  room,  the  second  in  one 
with  a  very  high  ceiling.  The  first  can  be  remedied  only  slightly  at  best,  the  latter  can  be  im- 
proved by  the  use  of  reflectors  behind  and  above  the  speaker.  On  the  other  hand,  should  the 
sound  be  loud  but  confuscil,  due  to  a  perceptible  prolongation,  the  difficulty  arises  from  there 
being  reflecting  surfaces  either  too  far  distant  or  improperly  inclined.  Proc.  .\merican  Insti- 
tute of  .\rcliitects.  p.  39,  1898. 


ABSORBING  POWER  OF  WALL-SLTiFACES  13 

will  be  given,  and  it  will  be  shown  that,  by  very  different  lines  of 
attack,  starting  from  diflFerent  data,  the  same  numerical  results  are 
secured.  Tables  will  be  given  of  the  absorliing  power  of  various 
wall-surfaces,  of  furniture,  of  an  audience,  and  of  all  the  materials 
ordinarily  found  in  any  (luaiilily  in  an  auditorium.  Finally,  in 
illustration  of  the  calculation  of  reverberation  in  advance  of  con- 
struction, will  be  cited  the  new  Boston  Music  Hall,  the  most  interest- 
ing case  that  has  arisen. 


ABSORBIXC;  POWER  OF  WALL-SURFACES 

In  the  introductory  article  the  problem  was  divided  into  considera- 
tions of  loudness,  of  distortion,  and  of  confusion  of  sounds.  Con- 
fusion may  arise  from  extraneous  disturbing  sounds  —  street  noises 
and  the  noise  of  ventilating  fans  —  or  from  the  prolongation  of  the 
otherwise  discrete  sounds  of  nuisic  or  the  voice  into  the  succeeding 
sounds.  The  latter  phenomenon,  known  as  reverberation,  results 
in  what  may  be  called,  with  accuracy  and  suggestiveness,  residual 
sound.  The  (Imalion  of  I  his  residual  .sound  was  shown  to  depend 
on  the  amount  of  ab.sorbing  material  inside  the  room,  and  also,  of 
course,  on  the  absorbing  and  transmitting  power  of  the  walls;  and 
a  method  was  outlined  for  tleternu'ning  the  absorbing  power  of  the 
former  iu  terms  of  the  absorbing  power  of  some  material  chosen  as 
a  standard  and  used  in  a  preliminary  calibration.  A  moment's  con- 
sideration demonstrates  that  this  method,  which  is  of  the  general 
type  known  as  a  "substitution  method,"  while  effective  in  the  de- 
termination of  the  absorbing  power  of  furniture  and  corrective 
material,  aiul,  in  general,  of  anything  that  can  be  brought  into  or 
removed  from  a  room,  is  insufficient  for  determinating  the  absorb- 
ing jiower  of  wall-surfaces.  'J'his,  the  absorbing  power  of  wall- 
surfaces,  is  the  subjt'cl  of  the  present  ])ai)er;  aiul  as  the  method  of 
determination  is  an  evlensiou  of  llic  abovi'  work,  an<l  finds  its  justi- 
fication in  the  striking  consistency  of  the  results  of  the  observations, 
a  nu)re  clal)orate  description  of  the  experimental  method  is  desirable. 
A  proof  of  the  accuracy  of  every  step  taken  is  especially  necessary 
in  a  subject  concerning  which  theory  luus  been  so  largely  uncon- 
trolled speculation. 


1  I  UKVKHBKRATIOX 

Kiirly  ill  tlic  invest ipitioii  if  was  found  tliat  nu-asurenients  of 
tlu"  IfiiK'li  of  *'""'  <liiriiif,'  which  u  sound  was  au(lil)k'  after  tlie  source 
had  erased  gave  j)roniising  results  whose  larger  inconsistencies  could 
1m'  trac-<'d  directly  to  the  distraction  of  outside  noises.  On  repeating 
the  work  during  the  most  ((iiiet  part  of  the  nigiit,  between  half-past 
twelve  and  five,  and  using  refined  recording  apparatus,  the  minor 
irregidarities,  due  to  n-laxed  attention  or  other  personal  variations, 
were  surprisingly  small.  To  seciin-  accuracy,  however,  it  was  neces- 
sary to  suspend  work  on  the  apjiroach  of  a  street  car  within  two 
blocks,  or  on  the  p;ussing  of  a  train  a  mile  distant.  In  Cambridge 
these  interruptions  were  not  serious;  in  Boston  and  in  New  York 
it  was  necessary  to  snatch  observations  in  very  brief  intervals  of 
c|uiet.  In  every  case  a  single  determination  of  the  duration  of  the 
residual  sound  was  based  on  the  average  of  a  large  number  of 
observations. 

An  organ  pijie,  of  the  gemshorn  stop,  an  octave  above  middle  c 
(51'-2  vibration  fre(|uencv)  was  used  as  the  source  of  .sound  in  some 
preliminary  experiments,  and  has  been  retained  in  subsequent  work 
in  the  absence  of  any  good  reason  for  changing.  The  wind  supply 
from  a  double  tank,  water-sealed  and  noiseless,  was  turned  on  and 
off  the  organ  i)ii)e  by  an  electro-pneumatic  valve,  designed  by  ^Vlr. 
George  S.  Ilutchings.  and  similar  to  that  u.sed  in  his  large  church 
organs.  The  electric  current  controlling  the  valve  also  controlled 
the  chronograph,  and  was  made  and  broken  by  a  key  in  the  hands 
of  the  observer  from  any  part  of  the  room.  The  chronograph  em- 
ployed in  the  later  experiments,  after  the  more  usual  patterns  had 
l>een  tried  and  discarded,  was  of  sjx'cial  design,  and  answered  well 
the  requirements  of  the  work  —  perfect  noiselessness,  portability, 
and  capacity  to  measure  intervals  of  time  from  a  half  second  to  ten 
seconds  with  considerable  accuracy.  It  is  shown  in  the  adjacent 
diagram.  The  current  whose  cessation  stopped  the  sounding  of  the 
organ  pii)e  also  gave  the  initial  record  on  the  chronograph,  and  the 
only  duty  of  the  observer  was  to  make  the  record  when  the  sound 
ceased  to  be  audible. 

While  the  supreme  test  of  the  investigation  lies  in  the  consistency 
and  simi)licity  of  the  whole  solution  us  outlined  later,  three  pre- 
liminary criteria  are  found  in  (1)  the  agreement  of  the  observations 


ABSORBINC;  POWER  OF  WALL-SURFACES 


15 


ol)tiiined  at  one  sitting,  ('-2)  the  agreement  of  the  results  obtained 
on  different  niglits  and  after  tlie  lapse  of  months,  or  even  years,  l)y 
the  same  observer  under  simihir  conditions,  and  (3)  the  agreement 
of  independent  determinations  by  different  observers.  The  first 
can  best  be  discussed,  of  course,  by  the  recognized  physical  methods 
for  examining  the  accuracy  of  an  extended  series  of  observations; 


l*'l<:.    !.     <'lin)n()^ni])Ii,  l)aU»T\',  and  air  rcst-rvoir,  Ihr  liiltrr  surniounti'd 
l).v  llir  rli<lr(>-|)ii<iiiiiatit'  valve  and  orpin  pipe. 

and  the  result  of  such  cxanu'nation  is  as  follows:  Each  dctcruiiualion 
being  I  lie  incaM  of  aixiul  Iwcuty  ()bscr\al  ions  uiidi-r  conditions  such 
thai  llic  audililc  diiialiOu  of  llic  loichial  souiui  was  4  seconds,  the 
average  devialioii  of  llic  single  ol>ser\ations  from  the  mean  was  .11 
seconds,  and  the  maximum  de\iation  was  .31.  The  ctJinputed 
"j)robable  error"  of  a  single  determination  Wius  about  AH  seconds; 
.IS  a  mailer  of  fact,  the  average  tleviation  of  t«'n  determinations 
from  I  lie  mean  of  I  he  leu  was  .03  seconds,  and  the  iiia\imuiii  de\i- 


16  hkvi;i{|{i;hatiox 

at  ion  was  .().>.  Tlif  roason  for  this  accuracy  will  l)e  discussed  in  a 
suhsoqut'iit  pajMT.  The  prohal)lc  error  of  the  mean,  thus  calculated 
from  the  tleviatious  of  the  single  ol).servations,  covers  only  those 
variaMe  errors  as  likely  to  increase  as  to  decrease  the  final  result. 
Fixed  iiislninH-ntal  errors,  and  the  constant  errors  commonly  re- 
ferretl  to  by  the  term  "personal  factors"  are  not  in  this  way  exposed. 
They  were,  however,  rejjeatedly  tested  for  by  comparison  with  a 
dock  l>eatiMf;  seconds,  and  were  very  satisfactorily  shown  not  to 
amount  to  more  than  .0^2  seconds  in  their  cunmlative  eft'ect.  Three 
typ«'s  of  chronographs,  and  three  kinds  of  valves  between  the  organ 
j)ipe  and  the  wind  chest  were  used  in  the  gradual  development  of 
the  experiment,  and  all  gave  for  the  same  room  very  nearly  the  same 
final  results.  The  later  instruments  were,  of  course,  better  and  more 
accurate. 

The  second  criterion  mentioned  above  is  abundantly  satisfied  by 
the  experiments.  Observations  taken  every  second  or  third  night 
for  two  months  in  the  lecture-room  of  the  Fogg  Art  ^Museum  gave 
practically  the  same  results,  varying  from  .5.45  to  o.G-Z  with  a  mean 
value  of  5.57  seconds,  a  result,  moreover,  that  was  again  obtained 
after  the  lapse  of  one  and  then  of  three  years.  Equally  satisfactory 
agreement  was  obtained  at  the  beginning  ami  at  the  end  of  tlu^ee 
years  in  Sanders  Theatre,  and  in  the  const  ant -temperature  room 
of  the  Physical  Laboratory. 

Two  gentlemen,  who  were  already  somewhat  skilled  in  physical 
observation,  Mr.  Gifford  LeClear  and  Mr.  E.  D.  Densmore,  gave 
the  necessary  time  to  test  the  third  point.  After  several  nights' 
practice  their  results  differed  but  slightly,  being  .08  .seconds  and 
.10  seconds  longer  than  those  obtained  by  the  writer,  the  total 
duration  of  the  sound  being  4  seconds.  This  agreement,  showing 
that  the  results  are  i>robably  very  nearly  those  that  would  be  ob- 
tained by  any  auditor  of  nornud  hearing,  gives  to  them  additional 
interest.  It  should  be  stated,  however,  that  the  final  development 
of  the  subject  will  adapt  it  with  perfect  generality  to  either  normal 
or  abnormal  acuteness  of  hearing. 

Almost  the  first  step  in  the  investigation  was  to  establish  the 
following  three  fundamentally  important  facts.  Later  work  has 
proved  these  fundamental  facts  far  more  accurately,  but  the  original 


ABSORBING  POWER  OF  WALL-SURFACES 


17 


experiments  are  here  given  as  being  those  upon  which  the  conclu- 
sions were  based. 

The  duration  of  audibility  of  the  residual  sound  is  nearly  the  same 
in  all  parts  of  an  auditorium.  —  Early  in  the  investigation  an  ex- 
periment to  test  this  point  was  made  in  Steinert  Hall,  in  Boston. 
The  source  of  sound  remaining  on  the  platform  at  the  point  marked 


Fig.  2.    Steinert  Hall,  Boston :  position  of  air  reservoir 
and  organ  pipe  at  ();  ixisitions  of  observer  1-8. 

0  in  the  diagram,  observations  were  made  in  succession  at  the  points 
marked  1  to  8,  with  the  results  shown  in  the  table: 

Station 

1 

2 

8 

4 


Durutioi) 

Slatiou 

Duratioo 

2.12 

5 

2.23 

2.17 

6 

2.27 

2.23 

7 

2.20 

2.20 

8 

2.26 

Oil  first  in.spection  these  results  seem  to  indicate  that  the  duration 
of  audibility  is  very  slightly  greater  at  a  distance  from  the  source, 
and  it  would  be  easy  to  explain  this  on  the  theory  that  at  a  distance 
the  ear  is  less  exhau.sted  by  the  rather  loud  noise  while  the  i)ipe  is 
sounding;  but,  ius  a  matter  of  fact,  tliis  is  not  the  ease,  and   the 


18 


in;M:Hi{KHA'riox 


variations  tluTc  sliown  arc  williiii  the  limits  of  accuracy  of  the 
a|)|)aratiis  (•iii|)l()yf(l  and  the  stcill  attained  tlnis  early  in  the  in- 
vest i>;at  ion.  Numerous  later  experiments,  more  accurate,  hut  not 
especially  directed  to  this  point,  have  verified  the  above  general 
statement  {|uite  conclusively. 

The  duration  of  audihUUy  is  ncarlij  iudepetideut  of  Ihc  position  of 
the  souri-r.       'Die  oli^crvrr  remaining;  at  the  point  marked  0  in  the 

diafiram  of  the  large  lecture-room 
of  the  Jefferson  Physical  Labora- 
tory, the  organ  i)ij)e  and  wind  chest 
were  moved  from  station  to  sta- 
tion, as  indicated  l)y  the  ninnljcrs 
1  to  (i,  witli  the  results  shown  in' 
the  table: 

Station  Duration 

1 3.90 

■2 4.00 

:? 3.90 

4 3.98 

,"> 3.95 

(i 3.96 


m 

R 

a 

R 

R 

H 

1 

^^^     1           M           M           II            II            II           1     1 

"-- —    sl 

nODOS 

•> 

UUUuL 

0 
0 

1 

3  "„"" 


,.      ,    ,    .  ,  ,,         r.1     ■    ,  The  cfficiencij  of  an  absorbent  in 

rl<i.  .».    Lfcturf-r<)<)tii.  Ji-ticrson   I'hysical  _  _ 

ljiU)ratory:  position  of  obsi-rvcr  at  0;    reducing  the  duration  of  the  residual 

position.,  of  air  n-MTVoir  and  organ  pipe     ^.,^,^,,^,    '-^.^    ^^„^;^^    ordinary     cirCUm- 

stances,  nearly  independent  of  its 
position.  —  Fifty  meters  of  cretonne  dotli  drajjcd  on  a  scaffolding 
under  the  rather  low  ceiling  at  the  back  of  the  lecture-room  of 
the  Fogg  Museum,  as  shown  in  the  next  diagram,  reduced  the 
audil)le  duration  of  the  residual  sound  by  very  nearly  the  same 
amount,  regardless  of  the  section  in  which  it  hung,  as  shown  in  the 
following  table,  the  initial  duration  being  5.57  seconds: 


Section 
1.  . 

2.. 
3.. 
4.. 


Duration 

.  4.88 

.  4.83 

.  4.92 

.  4.85 


In  some  later  experiments  five  and  a  half  times  as  much  cretonne 
draped   on   the   scaffolding   reduced    the   audible   duration   of   the 


ABSORBING  POWER  OF  WALL-SURFACES 


1!) 


residual  .sound  to  3. "25  seconds;  and  when  hung  fully  exposed  in 
the  high  dome-like  ceiling,  gave  3.29  seconds,  confirming  the  above 
statement. 

These  facts,  simple  when  proved,  were  by  no  means  self-evident 
so  long  as  the  problem  was  one  of  reverberation,  that  is,  of  succes. 
sive  reflection  of  sound  from  wall  to 
wall.  Tlie\- indicated  that,  al  Icaslwilli 
reference  to  auditoriums  of  not  too 
great  diincnsions,  another  jioint  of  view 
woukl  be  more  suggestive,  that  of  re- 
garding the  whole  as  an  energy  problem 
in  which  the  source  is  at  tlie  organ 
pipe  and  the  decay  at  the  walls  and 
at  tlie  contained  absorbing  material. 
The  above  results,  then,  all  point  to 
the  evident,  but  pcrliajis  not  appreci- 
ated, fact  that  the  dispersion  of  sound 
between  all  j)arts  of  a  hall  is  very  nipid 
in  comparison  with  the  total  time  re- 
quired for  its  complete  absorjjfion,  and 
tiiat  in  a  very  short  time  after  the 
source  has  cea.sed  the  intensity  of  the 
residual  sound,  except  for  the  phenom- 
enon of  interference  to  be  considered 
later,  is  very  nearly  the  same  every- 
where in  the  room. 

I'liis  much  being  determined,  the 
investigation  was  continued  in  the  fol- 
lowing manner:  Cushions  from  San- 
ders Theatre  were  transferred  to  llie 
lobby  of  I  lie  lecture-room  of  the  J''ogg 
]V[u.seum;  a  very  few  were  brought  into  the  room  and  spread  along 
the  front  row  of  seats;  the  duration  of  audiltilily  of  the  residual 
sound,  diminished  1)_\  llic  inl  iddiiclioii  of  lliis  additional  al)sorbeiit, 
was  determined,  and  liie  total  length  of  cushion  was  measured.  The 
next  row  of  seats  was  then  (•<)vere<l  in  the  sanii-  manner  and  the  two 
observations  made       length   of  cushion   and  iluration  of  resitlual 


Fig.  i.  Lectur»'-room,  Fopg  .\rt 
Museum:  position  of  ob.sorvcr at 
();  positions  of  absorbent  ul  1-4, 
ami  in  tlie  dome. 


20  HEVKIiHKHATIOX 

sound.  Tliis  was  rciH-atcd  till  cushions  covered  all  the  seats.  This 
work  wjui  at  first  undertaken  solely  with  the  intention  of  determin- 
ing the  relative  merits  of  different  absorbing  materials  that  might 
be  plac-e<l  in  the  room  !is  a  corrective  for  excessive  residual  soimd, 
and  the  aeeounl  of  this  ai)plieation  is  ffWcn  in  the  introductory 
paper.  A  subsequent  study  of  these  and  similar  results  obtained  in 
many  other  rooms  has  shown  their  applicability  to  the  accurate 
(1.  hrmination  of  the  absorbing  luiwcr  of  wall-surfaces.  This  appli- 
cation may  be  shown  in  a  i)urely  analytical  manner,  but  the  expo- 
sition is  greatly  helped  by  a  graphical  representation.  The  nuxnner 
in  which  the  tluralion  of  the  residual  sound  in  the  Fogg  lecture- 
room  is  dependent  on  the  amount  of  absorbing  material  present  is 
shown  in  the  following  table: 

UiiRth  Duration  of 

of  Cushion  Residual  Sound 

in  MclCTJ  "■  i^onds 

0 5.61 

8 5.33 

17 4.94 

38 4.56 

44 4.21 

63 3.94 

83 3.49 

104 3.33 

128 3.00 

145 2.85 

162 2.64 

189 2.36 

213 2.33 

242 2.22 

This  table,  represented  graphically  in  the  conventional  manner  — 
length  of  cushion  jilotted  horizontally  and  duration  of  sound  verti- 
cally—  gives  points  through  which  the  curve  may  be  drawn  in  the 
accompanying  diagram.  To  disco\'er  the  law  from  this  curve  we 
represent  the  lengths  of  cushion  by  .r,  and  the  corresponding  dura- 
tions of  sound,  the  vertical  distances  to  the  curve,  by  t.  If  we  now 
seek  the  formula  connecting  .r  and  t  that  most  nearly  expresses  the 
relationship  represented  by  the  above  curve,  we  find  it  to  be 
(a  -|-  x)t  =  k,  which  is  the  familiar  formula  of  a  rectangular  hyper- 
bola with  its  origin  displaced  along  the  axis  of  .r,  one  of  its  asymp- 
totes, by  an  amount  a.    To  make  this  formula  most  closely  fit  our 


ABSORBING  POWER  OF  WALL-SURFACES 


21 


curve  we  must,  in  this  case,  give  to  the  constant,  a,  the  numerical 
value,  146,  and  to  /.•  tlie  value,  81.'5.  The  accuracy  with  which  the 
formula  represents  the  curve  may  be  seen  by  comparing  the  dura- 
tions calculated  by  the  formula  with  those  determined  from  the 
curve;  they  nowliere  diiVer  by  more  than  .04  of  a  si-cond,  and  ha\e, 
on  an  average,  a  difference  of  only  .02  of  a  second.  This  is  entirely 
satisfactory,  for  the  calculated  points  fall  off  from  the  curve  by 
scarcely  the  l)readth  of  the  pen  jjoint  with  which  it  was  drawn. 

The  determination  of  the  ab.sorbing  power  of  the  wall-surface 
depends  on  the  interpretation  of  the  constant,  a.    In  the  formula, 


'"^^ 

X 

•A. 

■^ 

^-, 

■"— 

^ 

10 
9 

8 
7 
6 
5 
4 
3 
2 
1 

"20  40  60  80  100  120  140  160  180  200  220  240  260  280  300 

Length  of  cushions  in  meters 

Fig.  5.    Curve  showing  the  relation  of  tlie  duration  of  the  residual 
sound  to  the  added  absorbing  material. 

the  position  of  a,  indicating  that  x  is  to  be  atlded  to  it,  suggests 
that  .(■  and  a  are  of  a  like  nalurc,  and  llial  <t  is  a  measure  of  the 
absorbing  power  of  the  bare  room;  in  order  to  determine  the  curve 
this  was  increa.sed  by  the  introduction  of  the  cushions.  This  is 
even  better  shown  by  the  diagram  in  which  the  portion  of  the  curve 
experimentally  determined  is  fitted  inio  llie  curve  as  a  whole,  and 
a  and  x  are  indicated.  Thus,  the  absorbing  power  of  the  room  — 
the  walls,  partly  plaster  on  stone,  partly  plaster  on  wire  lath,  the 
windows,  the  skyliglil,  I  lie  floor  —  was  equivalent  lo  14(»  rimning 
meters  of  Sanders  Theatre  cushions. 

The  last  .statement  shows  llir  necessity  for  two  Mib>i(li:iiy  in- 
vestigations. The  first,  to  express  the  residts  in  .some  more  i)ernia- 
nent,  more  tmiversally  availal)le,  and,   if  po.ssible,  more  ab.solute 


o^ 


HKVKHHKRATION 


unit  Ihiin  llu-  cushions;   tlic  otIuT,  lo  apimrlioii  tin-  total  al)sorbing 
power  aiMonj,'  tin-  various  conipoiu'nt.s  of  the  structure. 

Tlif  transformation  of  results  from  one  system  of  units  to  an- 
otlier  necessitates  a  careful  study  of  both  systems.  Some  early 
experiments  in  \vlu<-li  the  cushions  were  placed  with  one  edfje  pushed 
jigaiust  the  hacks  of  the  settees  gave  results  whose  auonuilous 
character  suggested  that,  perhaps,  their  absorbing  power  depended 
not  merely  on  the  amount  present  but  also  on  the  area  of  the  sur- 
face exposed.  It  was  then  recalled  that  about  two  years  before, 
at   the  beginning  of  an  evening's  work,   the  first    lot   of  cushions 


10 

s 

■S      T 

c 


.5       5 

c 
.2      i 

S 

=  3 
2 
1 


\ 

\ 

\ 

\ 

'' 

[S 

V 

^ 

^ 

— — 

— 

— 

— 

so 
Walls 


160 


240  S20  400 

Cushions 


S60 


Fig.  6.  Curve  5  plotted  as  part  of  its  eorresponding  rectangular 
hypcrlx)la.  The  solid  part  was  determim^d  experimentally; 
the  displacement  of  this  to  the  right  measures  the  absorbing 
power  of  the  walls  of  the  room. 

brought  into  the  room  were  placed  on  the  floor,  side  by  side,  with 
edges  touching,  but  that  after  a  few  observations  had  been  taken 
the  cushions  were  scattered  about  the  room,  and  the  work  was 
rei)eate(l.  This  was  done  not  at  all  to  uncover  the  edges,  but  in 
the  primitive  uncertainty  as  to  whether  near  cushions  would  draw 
from  each  other's  supply  of  soimd,  as  it  were,  and  thus  diminish 
each  other's  efficiency.  No  furl  li.i-  t  bought  was  then  given  to  these 
discarded  observations  until  recalled  by  the  above-mentioned  dis- 
crejjancy.  'J'hey  were  sought  out  from  the  notes  of  that  period, 
and  it  was  found  that,  a.s  suspected,  the  absorbing  power  of  the 
cushions  when  touching  edges  was  less  than  when  separated.  Eight 
cushions  had  been  used,  and,  therefore,  fourteen  edges  had  been 


ABSORBING  POWER  OF  WALI^SURFACES  23 

touching.  A  record  was  found  of  the  length  and  the  breadth  of 
the  cushions  used,  and,  assuming  that  the  absorbing  power  was 
proportional  to  the  area  exposed,  it  was  possible  to  calculate  their 
thickness  by  comparing  the  audible  duration  of  the  residual  sound 
in  the  two  sets  of  observations;  it  was  thus  calculated  to  be  7.4 
centimeters.  On  stacking  up  the  same  cushions  and  measuring 
their  total  thickness,  the  average  thickness  was  found  to  be  7.2 
centimeters,  in  very  close  agreement  with  the  thickness  estinuited 
from  their  absorption  of  sound.  Therefore,  the  measurements  of 
the  cushions  should  be,  not  in  running  meters  of  cushion,  but  in 
square  meters  of  exposed  surface. 

For  the  purposes  of  the  present  investigation,  it  is  wholly  un- 
necessary to  distinguish  between  the  transformation  of  the  energj- 
of  the  sound  into  heat  and  its  transmission  into  outside  space. 
Both  shall  be  called  absorption.  The  former  is  the  special  accom- 
plishment of  cushions,  the  latter  of  open  windows.  It  is  obvious, 
however,  that  if  both  cushions  and  windows  are  to  be  classed  as 
absorbents,  the  open  window,  because  the  more  universally  acces- 
sible and  the  more  permanent,  is  the  better  unit.  The  cushions,  on 
the  other  hand,  are  by  far  the  more  convenient  in  practice,  for  it 
is  possible  only  on  very  rare  occasions  to  work  accurately  with  the 
windows  open,  not  at  all  in  summer  on  account  of  night  noises  — 
the  noise  of  crickets  and  other  insects  —  and  in  the  winter  only 
when  there  is  but  the  slightest  wind;  and  further,  but  few  rooms 
have  sufficient  window  surface  to  produce  the  desired  absorption. 
It  is  necessary,  therefore,  to  work  willi  cushions,  but  to  express  the 
results  in  open-window  units. 

Turning  now  to  the  unit  into  which  the  results  are  to  be  trans- 
formed, an  especially  quiet  winter  night  wjis  taken  to  determine 
whether  the  absorbing  power  of  open  windows  is  jjroportional  to 
the  area.  A  test  of  tiie  absorbing  power  of  seven  windows,  each 
1.10  meters  wide,  when  oix-iied  ."-iO,  .40,  and  .80  meter,  gave  results 
that  are  plotted  in  tiie  diagram.  The  points,  by  falling  in  a  straight 
line,  show  that,  at  least  for  moderate  i)readlhs,  the  al)sorbing 
power  of  open  windows,  as  of  cushions,  is  accurately  proi)ortional 
to  tlie  area.  Ex|)i'riments  in  several  rooms  especially  convenient 
for  the  purpo.se  determined  the  absorbing  power  of  the  cushions  to 


^4 


RKVKHHKRATIOX 


Ix-  .80  of  that  of  an  (-(lual  art-a  of  opt-n  windows.  Tlu-.so  cusiiions 
wiTf  of  hair,  covtrcd  witli  canvius  and  light  dunia.sk.  "Elastic 
Felt"  cu-shions  having  lufii  ii>*«'d  during  an  investigation  in  a  New 
York  church,  it  wjw  necessary  on  returning  to  Cand)ridgc  to  deter- 
mine their  ai>sorl)iiig  power.  This  was  acconii)iished  through  the 
c-ourtesy  of  the  manufacturers,  Messrs.  Sperry  &  Beale,  of  New 
York,  and  the  absorbing  power  was  found  to  be  .73  of  open-window 


u 

t 
• 

I* 

"t    4 

<    3 
2 

1 

/ 

f\ 

/ 

/ 

/ 

/ 

/ 

/ 

/ 

/ 

/ 

0 

.1 

J  .2 

B   Ji 

0    .4< 

0    .» 

0    .« 

3    .7 

>   .8< 

9    .»< 

)  1.00  1.10  1.20  130  1.40  1. 

Open  window 

Fig.  7.    The  absorbing  power  of  open  windows  plotted  against  the 
areas  of  the  openings,  showing  them  to  be  proportional. 

units  —  an  interesting  figure,  since  these  cushions  are  of  frequent 
use  and  of  standard  cliaracfer. 

Hereafter  all  results,  though  ordinarily  obtained  by  means  of 
cushions,  will  be  expres.sed  in  terms  of  the  absorbing  power  of  open 
windows  —  a  unit  as  permanent,  universally  accessible,  and  as 
nearly  absolute  as  possible.  In  these  units  the  total  absorbing 
power  of  the  walls,  ceiling,  floor,  windows  and  chairs  in  the  lecture- 
room  of  the  Fogg  Museum  is  75. .5. 

Next  in  order  is  the  apportionment  of  the  total  absorbing  power 
among  the  various  components  of  the  structure.  Let  ^i  be  the  area 
of  the  plaster  on  tile,  and  fli  its  absorbing  power  per  square  meter; 
Si  and  «2  the  corresponding  values  for  the  plaster  on  wire  lath;  S3 
and  03  for  window  surface,  etc.    Then 

«!  «1  +  02  «2  +  03  ^3  +  Oi  Si,  ctc.    =    75.5, 

Si,  St,  S3,  etc.,  are  known,  and  «i,  «2,  03,  etc.  —  the  coeflBcients  of 
absorption  —  are  unknown,  and  are  being  sought.     Similar  equa- 


APPROXIMATE  SOLUTION 


25 


tions  may  be  obtained  for  other  rooms  in  which  the  proportions 
of  wall-surface  of  the  varioiis  kinds  are  greatly  different,  until  there 
are  as  many  equations  as  there  are  unknown  quantities.  It  is  then 
possible  by  elimination  to  determine  the  absorbing  power  of  the 
variou.s  materials  used  in  construction. 

Through  the  kindness  of  Professor  Goodale,  an  excellent  oi)por- 
tunity  for  securing  some  fundamentally  interesting  data  was 
afforded  by  the  new  Botanical  Laboratory  and  Greenhouse  recently 
given  to  the  L^niversity.  These  rooms  —  the  office,  the  laboratory 
and  the  greenhouse  —  were  exclusively  finished  in  hard-pine  sheath- 
ing, glass,  and  cement;  the  three  rooms,  fortunately,  combined  the 
three  materials  in  very  tlifferent  proportions.  I'hey  antl  the  con- 
stant-temperature room  in  the  Physical  Laboratory  —  the  latter 
being  almost  wholly  of  brick  and  cement  —  gave  the  following 
data: 


Area  of 
Hard  Pine 
Sheathing 


Area  of  Glaas 


Area  of  Brick 
aod  Cement 


Combined 

Absorbing 

Power 


Office                     

127.0 

84.8 

12.7 

2.1 

7 

6 

80 

0 

0 

30 

So 

124 

8.37 

l.alHiratory 

Grci'iihouso 

Constant-temperature  room .  .  .  . 

5.14 
4.C4 
3.08 

This  table  gives  for  the  three  components  the  following  coefficients 
of  absorption:  hard  pine  sheathing  .058,  glass  .024,  brick  set  in 
cement  .023. 


APPROXIMATE  SOLUTION 

In  the  preceding  paper  it  was  shown  that  the  duration  of  the 
residual  sound  in  a  particular  room  was  proi)orti(>nal  inversely  to 
the  absorbing  power  of  the  bounding  walls  and  tlic  contained 
material,  the  law  being  expressed  closely  by  the  fornuda  {a  +  x)t 
=  Jc,  the  formula  of  a  displaced  rectangular  hyjHrbola.  In  the 
present  paper  it  is  proposed  to  show  that  this  fornuda  is  general, 
and  ajJijlicable  to  any  room;  that  in  adapting  it  to  different  rooms 
it  is  only  necessary  to  change  the  value  of  the  et)nstant  of  inverse 
proportionality  /.•;    tlmt  /,•  is  in  turn  proportional  to  the  volume  of 


^.Mi 


RE^TRBERA^'I()X 


ll„-  n«.m.  iK'ing  equal  to  about  .171V  in  the  present  experiments, 
hut  ch-peiident  on  the  initial  intensity  of  the  sound;  and  finally, 
that  hv  sul)stiluting  I  lie  value  of  k  thus  determined,  and  also  the 


^     a 

5 




\! 

■n 

^^ 

--■^ 

^ 

=*=: 

^ 

"l 

S.^ 

~7 . 



, 

^. 

"^^ 

■==! 

=y: 

~S, 



-^ 

^^ 

r^ 

=— 

■-2-. 

-1-. 



= 

___ 

t 

I 

i 

i 

i 

i 

' 

» 

9      10    11     12 

L3     19     1 

Longth  of  cushions  in  meters 

Fig.  8.    Curves  showing  the  relation  of  the  duration  of  the  residual 
sound  to  the  added  absorbing  material,  —  rooms  1  to  7. 


c 


e 
.S    2 


— ^ 

V 

\ 

"^ 

^ 

^ 

K 

"-- 

-11. 

tir^ 

^8, 

-12- 

, 

" 

H 

■^ 

"*" 

0    10  20  30  «0  $0  60  TO  80  90  100  110  UO  130  140  150 

Length  of  cushions  in  meters 

Fig.  9.    Curves  showing  the  relation  of  the  duration  of  the  residual 
sound  to  the  added  absorbing  material,  —  rooms  8  to  12. 


value  of  a,  the  absorbing  power  of  the  walls,  and  of  x,  the  absorbing 
power  of  the  furniture  and  audience,  it  is  possible  to  calculate  in 
advance  of  construction  the  duration  of  audibility  of  the  residual 
sound. 


APPROXI.MATE  SOLUTION 


27 


The  truth  of  the  first  proposition  —  the  general  appUcahiUty 
of  the  hyperbohc  hiw  of  inverse  proportionaUty  —  can  be  satis- 
factorily shown  by  a  condensed  statement  of  the  results  obtained 
from  data  collected  early  in  tiie  investigation.  These  observations 
were  made  in  rooms  varying  extremely  in  size  and  shape,  from  a 
small  committee-room  to  a  theatre  having  a  seating  capacity  for 
nearly  fifteen  hundred.  Figures  8  and  9  give  the  curves  experi- 
mentally  determined,   the  duration   of   audibility   of   the   residual 


0    10  20  30  40  50  60  TO  80  90  100  110  120  130  140  160 
120     160     240     300     360     420 
S40     720     900     1080    1360 

Total  absorbing  material 

Fig.  10.  The  curves  of  Figs.  8  and  !)  enteretl  as  parts  of  their  corre- 
sponding rectangular  h\-perlx)las.  Thre<;  .scales  are  employed  for 
the  volumes,  by  groups  1-7,  8-11,  and  H. 

sound  l)eing  plotted  against  running  meters  of  cushions.  Two 
diagrams  are  given  in  order  to  employ  a  smaller  .scale  for  the  larger 
rooms,  this  scale  l)eing  one-tenth  the  other;  and  even  in  this  way 
there  is  shown  but  one-quarter  of  the  curve  actually  obtained  in 
rooms  numbered  11  and  l'-2,  the  Fogg  Art  Museum  lecture-room 
and  Sanders  Theatre.  In  Fig.  10  each  curve  is  entered  as  a  i)arl 
of  its  corresi)onding  hyperbola  referred  to  its  asymptotes  as  axes. 
In  this  case  three  scales  are  employed  in  order  to  show  the  details 
luor*'  clearly,  the  results  oljtaincd  in  rooms  1  to  7  on  one  scale.  S  to 
1 1  on  another,  and  l'-2  on  a  third,  the  three  scales  being  proj)ortionaI 
to  one,  three  and  nine.  The  continuous  i)ortions  of  the  curves 
show   the   |>,irts   (Ictcrniiiied   cxpcriMifulallx'.      V.ViW    with   the  scale 


?8 


RK\ KUBKHATIOX 


thus  clianRcd  only  a  very  small  portion  of  the  experimentally  de- 
termined i.arts  of  eurves  11  ami  hi  are  shown.  Figures  11  to  10, 
inelusive.  all  drawn  to  the  same  scale,  show  the  great  variation  in 
size  and  shai)e  of  the  rooms  tested;  and  the  accompanying  notes 
^ive  for  ( iich  the  maximum  dei)arture  and  average  departure  of  the 
curve,  exi)eriineiilally  determined,  from  the  nearest  true  liyi)erbola. 
1.  Committee-room,  I'niversity  Hall;  plaster  on  wood  lath, 
wood  dado;  volume,  65  cubic  meters;  original  duration  of  residual 
sound  before  the  introduction  of  any  cushions,  2.82  seconds;   maxi- 


" 

BB 

a 

no 

!  1 

a 

lit     ■  1  u 

|q  1         11-11         J| 

4 


1 

n 

W 

n 

1 

IP  i 1  CD  1 1  (—1 

1 1 

C 

lot          1  [=1  1         1  1  ID  (         111 

5  6  7 

Fig.  11.  1.  CommiUpc-room.  4.  Laboratory,  Hotanic  Gardeu.s.  3.  Office, 
Hotaiii((!ar(l(ii.s.  i.  Hcoordcr's  Ofike.  5.  Greenliou.se.  6.  Dean's 
H<M>m.     7.  Clerk's  RiHini. 


iinmi  departure  of  experimentally  determined  curve  from  the  nearest 
hyperbola,  .0!)  second;   average  dej)arture,  .03  second. 

2.  Laboratory,  Botanic  Gardens  of  Harvard  University;  hard 
pine  walls  and  ceiling,  cement  floor;  volume,  82  cubic  meters; 
original  duration  of  the  residual  sound,  2.39  seconds;  maximimi 
departure  frdiii  hyperbola,  .09  second;  average  departure,  .02 
second. 

3.  Office,  Botanic  Gardens;  hard  pine  walls,  ceiling  and  floor; 
volume,  99  cubic  meters;  original  duration  of  residual  sound,  1.91 
.seconds;  maximum  departure  from  hyperbola,  .01  second;  average 
departure.  .00  second. 

4.  Recorder's  OfKce,  University  Hull;  i)laster  on  wood  lath. 
wood  dado;  volume,  102  cubic  meters;  original  duration  of  residual 
sound,  3.68  seconds;  maximum  departure  from  hyperbola,  .10 
second;  average  departure,  .04  second. 


APPROXnrATE  SOLUTION 


29 


5.    Grot'iihousc,  Botanic  Gardens;  glass  roof  and  sidos,  cement 
floor;     volume,    l;54   eubie   meters;     original    duration    of   residual 


l'"iG.   IZ.     I'uculty-room. 

sound,   4.40   seconds;    maximum   departure   from   hyperbola,    .08 

second;  average  dejjarture,  .0.'5  second. 

G.    Dean's  Room,  University  Hall;    ])lasler  on  wood  lalh,  wood 
dado;    volume,   166  cubic  meters;    original   duration    of  residual 


Fig.   13.     I^'oturc-rooin. 


sound,   3.38    seconds;    maxinunii    (le])arlure   from    hyperbola,    .06 
second;  average  departure,  .01  second. 

7.   Clerk's  Room,  University  Hall;   plaster  on  wood  lath,  wood 
dado;     volume,   '■2'21    eubie   meters;    original    diu'ation   of   residual 


I'ui.   11.     Ijiborutory. 

sound,    4.10   .seconds;     maximum    dejiartun-    from    hyjx'rbola.    .10 
second;    average  dej)arlure.  AH  seeoiul. 


so 


IJKVKUBKHATION 


S.  Faculty-room,  I'liiversity  Hall;  plaster  on  wood  lath,  wood 
dado;  voiimu-,  1.480  nihic  meters;  original  duration  of  residual 
sound,  7.04  seconds;  maximum  departure  from  hyperbola,  .18 
second;   average  departure,  .08  second. 

!».  Ix'cture-room,  Room  1,  Jefferson  Physical  Laboratory; 
brick  walls,  plaster  on  wood  lath  ceiling;  furnished;  volume, 
1,6;50   cubic    meters;     original    duration    of    residual    sound,    3.91 


Fig.  15.    Leclure-room. 

seconds;  maximum  departure  from  hyperbola,  .10  second;   average 
departure,  .04  second. 

10.  Large  Laboratory,  Room  41,  Jefferson  Physical  Laboratory; 
brick  walls,  plaster  on  wood  lath  ceiling;  furnished;  volume, 
1,960  cubic  meters;  original  duration  of  residual  sound,  3.40  seconds; 
maximum  departure  from  hyiierbola,  .03  second;  average  depar- 
ture, .01  second. 

11.  Lecture-room,  Fogg  Art  ^Luseum;  plaster  on  tile  walls, 
plaster  on  wire-lath  ceiling;  volume,  2,740  cubic  meters;  original 
duration  of  residual  sound,  5.61  seconds;  maximum  departure  from 
hyperbola,  .04  second;  average  departure,  .02  second.  The  ex- 
periments in  this  room  were  carried  so  far  that  the  original  duration 
of  residual  sound  of  5.61  seconds  was  reduced  to  .75  second. 

12.  Sanders  Theatre;  plaster  on  wood  lath,  but  with  a  great 
deal  of  hard-wood  sheathing  used  in  the  interior  finish;  volume, 
9,300   cubic   meters;    original   duration   of   residual    sound,    3.42 


APPROXIMATE  SOLUTION 


31 


seconds;  maximum  departure  from  hyperbola,  .07  second;  average 
departure,  .02  second. 

It  thus  appears  that  the  iiyperbolic  hiw  of  inverse  proportion- 
ality holds  under  extremely  diverse  conditions  in  regard  to  the  size, 
shape  and  material  of  the  room.  And  as  the  cushions  used  in  the 
calibration  were  placed  about  (juite  at  random,  it  also  apjjears  that 
in  rooms  small  or  large,  with  high  or  low  ceiling,  with  flat  or  curved 


Fig.  16.    Sanders  Theatre. 


walls  or  ceiling,  even  in  rooms  with  galleries,  the  cushions,  wherever 
placed  —  out  from  under  the  gallery,  under,  or  in  the  gallery  — 
are  nearly  ec(ually  efKcacious  as  absorbents.  This  merely  means, 
however,  that  the  efficacy  of  an  absorbent  is  independent  of  its 
position  when  the  problem  under  consideratii)ii  is  tliat  of  reverbera- 
tion, and  that  the  sound,  disjuTsed  by  regular  and  irregular  reflec- 
tion and  by  diffraction,  is  of  nearly  the  same  intensity  at  all  parts  of 
the  room  soon  after  the  source  has  ceased;  and  it  will  be  the  object 
of  a  .sul)sc(iii(iit  i).i]icr  l<»  show  llial  in  respect  to  Ihr  iiiilial  distri- 
bution of  the  sound,  and  also  in  respect  to  discrete  echoes,  the  posi- 
tion of  the  absorbent  is  a  matter  of  prime  importance. 


32 


Ri:vi;i{|{i:i{Ari()\ 


Having  shown  that  tho  hyin-rbolii'  law  is  a  gi-neral  one,  interest 
centers  in  the  parameter,  /.-,  the  constant  for  any  one  room,  but  vary- 
ing from  room  lo  room,  as  the  following  table  shows: 


Boom 

1.  Comniittcc-rooni,  University  Hall..  . 

•i.  Ijiltorutory,  Holanic  Gardens 

3.  Ortic-e,  boUmic  Gardens 

4.  Recorder's  Office 

5.  Greenhouse,  Botanic  Gardens 

C.  Dean's  Kooin 

7.  Clerk's  Room 

8.  Faculty-room 

9.  I<ecture-room,  Jefferson  Physical  Lab- 

oratory, 1 

10.  Laboratory,  Jefferson  Physical  Lab- 

oratory, 41 

11.  FoKS  LiM-tu  re-room 

12.  Sanders  Theatre 


Volume 


65 
82 
99 

in-2 

134 

166 

221 

1,480 

1,630 

1,960 
2,740 
9,300 


Absorbing  Power  of 
Walls,  etc.,  =  a 


4.76 
4.65 
8.08 
.5.91 
5.87 
7.50 
10.6 
34.5 

69.0 

101.0 

75.0 

465.0 


Parameter  k 


13.6 
11.1 
15.4 
21.8 
25.8 
25.4 
43.5 
24.'5.0 

270.0 

345.0 

425.0 

1,590.0 


The  values  of  the  absorbing  jjower,  a,  and  the  parameter,  k,  are 
here  expressed,  not  in  terms  of  the  cushions  actually  used  in  the 
experiments,  l)ut  in  ti-rms  of  the  o])en-window  units,  sliown  to  be 
preferable  in  the  preceding  article. 

In  the  diagram.  Figure  17,  the  values  of  A'  are  plotted  against  the 
corresponding  volumes  of  the  rooms;  here  again  three  different 
scales  are  employed  in  order  to  magnify  the  results  obtained  in  the 
smaller  rooms.  The  resulting  straight  line  shows  that  the  value  of 
/,■  is  proportional  to  the  volume  of  the  room,  and  it  is  to  be  observed 
that  the  hirgest  room  was  nearly  one  hundred  and  fifty  times  larger 
than  the  smallest.    By  measurements  of  the  coordinates  of  the  line, 

or  by  averaging  the  results  found  in  calculating  ~  for  all  the  rooms 

it  appears  that  J:  =  .171 F.  The  physical  significance  of  this  nu- 
merical magnitude  .171  will  be  exjjlained  later. 

This  simple  relationship  between  the  value  of  k  and  the  volume 
of  the  room  —  the  rooms  tested  varying  so  greatly  in  size  and 
shape  —  affords  additional  proof,  by  a  rather  delicate  test,  of  the 
accuracy  of  the  method  of  experimenting,  for  it  show\s  that  the  ex- 


APPROXIMATE  SOLUTION 


33 


perimentally  dettTmined  curvos  iijjproxiinate  not  merely  to  hyper- 
bolas but  to  a  .systematic  family  of  hyperbolas.  It  also  furnishes  a 
more  pleasing  prospect,  for  the  laljorious  handling  of  cushions  will 
be  unnecessary.  A  single  experiment  in  a  room  and  a  knowledge  of 
the  volume  of  the  room  will  furnish  sufficient  data  for  the  calcula- 
tion of  the  absorbing  powi'r  of  its  coinixjuents.  Conversely,  a 
knowledge  of  the  volume  of  a  room  and  of  the  coefficients  of  absorp- 
tion of  its  various  components,  including  the  audience  for  which  it 
is  designed,  will  enable  one  to  calculate  in  advance  of  construction 
the  duration  of  audibility  of  the  residual  sound,  which  measures 

u 


IM 

»11 

/ 

/ 

9O00  " 

11^0 

12600 

i-T 

i:  100 

lOj/ 

4 

i 

yi 

H    so 

/ 

tzoo 

1800        2400         3000 

1600 

4S00 

^ 

4 
/i 

6/ 

y6 

■ 

3 

0 

a 

DO 

4( 

M 

6( 

>0 

oluii 

8( 

IPS  r 

)0 

f  ro 

10 

iins 

«0 

u 

00 

14 

m 

Fit;.  17.     The  parameter,  t,  plotted  again.st   tlic  volumes  of  the 
rooms,  showing  the  two  proportional. 


that  acoustical  property  of  a  room  commonly  called  reverberation. 
Therefore,  tliis  [)li;isc  of  the  problem  is  solved  to  a  first  approxi- 
mation. 

The  fXi)Iaiialion  of  llic  fact  that  /,•  is  propoii  ioiial  to  \  is  fouiul 
ill  the  following  rciusoning.  Consider  two  rooms,  constructed  ot 
exactly  the  same  materials,  similar  in  relative  proportions,  but  one 
larger  than  the  other.  The  rooms  being  eiiii)ty,  .r,  the  absorbing 
l)ower  of  the  contained  material,  is  zero,  and  we  liave  «'  \'  =  /."' 
and  n"  l"  =  /.•".  Since  the  rooms  are  con.structcd  of  I  he  same 
iiialcrials  the  coclliciriits  of  alooi  |)l  ioii  arc  iln'  >aiiic,  >o  llial  (/'  and 
r/"are  pr()])ortioiial  to  the  .surfaces  of  llie  rooms,  that  is, to  the  .•M|Uares 


34  REMCRBERATION 

(if  tin-  linear  dimensions.  Also,  the  residual  sound  is  diminished  a 
certain  pereentage  at  eadi  reflection,  and  the  more  frequent  these 
refleetions  are  the  shorter  is  the  thiration  of  its  audibihly;  wlience 
/'  and  /"  are  inversely  proi)ortional  to  the  frequency  of  the  reflec- 
tions, and  luiice  directly  proportional  to  tlu-  linear  dimensions. 
Therefore,  A"'  and  A",  which  are  equal  to  a'  t'  and  a"  t",  are  propor- 
tional to  the  cuIh's  of  the  linear  dimensions,  and  hence  to  the 
volumes  of  the  rooms. 

Further,  when  the  shape  of  the  room  varies,  the  volume  remain- 
ing the  same,  the  number  of  reflections  per  second  will  vary.  There- 
fore, A-  is  a  function  not  merely  of  the  volume,  but  also  of  tlie  shape 
of  the  room.  But  that  it  is  only  a  slightly  varying  function,  com- 
paratively, of  the  shape  of  the  room  for  practical  cases,  is  shown  by 
the  fact  that  the  points  fall  so  near  the  straight  line  that  averages 

the  values  of  the  ratio  —  • 

The  value  of  A-  is  also  a  function  of  the  initial  intensity  of  the 
sound;  but  the  consideration  of  this  element  will  be  taken  up  in  a 
following  paper. 


RATE  OF  DECAY  OF  RESIDUAL  SOUND 

In  a  subsequent  discussion  of  the  interference  of  sound  it  w'ill  be 
shown  by  photographs  that  the  residual  sound  at  any  one  point 
in  the  room  as  it  dies  away  passes  through  maxima  and  minima, 
in  many  cases  beginning  to  rise  in  intensity  immediately  after  the 
source  has  ceased;  and  that  these  maxima  and  minima  succeed 
each  other  in  a  far  from  simple  manner  as  the  interference  system 
shifts.  On  this  account  it  is  quite  impossible  to  use  any  of  the  nu- 
merous direct  methods  of  measuring  sound  in  experiments  on  rever- 
beration. Or,  rather,  if  such  methods  were  used  the  results  would 
be  a  mass  of  data  extremely  diflicult  to  interpret.  It  was  for  this 
reason  that  attempts  in  this  direction  were  abandoned  early  in  the 
investigation,  and  the  method  already  described  adopted.  In 
addition  to  the  fact  that  this  method  only  is  feasible,  it  has  the 
advantage  of  making  the  measurements  directly  in  terms  of  those 
units  with  which  one  is  here  concerned  ^ — the  minimum  audible 


RATE  OF  DECAY  OF  RESIDUAL  SOUND 


35 


intensity.  It  is  now  proposed  to  extend  tliis  method  to  the  deter- 
mination of  tlie  rate  of  decay  of  the  average  intensity  of  sound  in 
the  room,  and  to  the  determination  of  the  intensity  of  the  initial 
sound,  and  thence  to  the  determination  of  tlie  mean  free  path  be- 
tween reflections,  —  all  in  i)reparation  for  tlie  more  exact  solution 
of  the  problem. 

The  first  careful  experiment  on  the  absolute  rate  of  decay  was 
in  the  lecture-room  of  the  Boston  Public  Library,  a  large  room. 


\ 

1 

\ 

\ 

\ 

a 

3     . 

\ 

\, 

^     ° 

s. 

\ 

\ 

>4 

\ 

\, 

V 

s 

\ 

S' 

^ 

V 

'V 

\ 

a 

"-- 

•■-^ 

N^ 

MUM 

UDIBl 

1    IKTt 

l«IT» 

"~- 

--. 

— , 

■--. 

-i- 

■-»-. 

-H-' 



---- 

-.- 

8.5    8.6    8.T   8.8    8.9    9.0    9.1    9.2    9.3    9.4    9.5    9.*    9.T    9.8    9.9    10. 

Time  in  seconds 

Fig.  18.  Decay  of  sound  in  the  lecture-room  of  the  Boston  Public 
Library  from  the  initial  sound  of  one,  two,  three,  and  four  organ 
pipes,  showing  only  the  last  second. 

fini.shed,  with  the  exception  of  the  platform,  in  material  of  very 
slight  absorbing  power  —  tile  ceiling,  plaster  on  tile  walls,  and 
polished  cement  floor.'  The  reverl)eration  was  very  great,  8.6!) 
seconds.  On  the  platform  were  placed  foin-  organ  pipes,  all  of  the 
same  pitch,  each  on  its  own  tank  or  wind  suj)ply,  and  each  having 
its  own  electro-pneumatic  valve.  All  these  valves,  however,  were 
connected  to  one  chronograph,  key,  and  battery,  so  that  one,  two, 
three,  or  all  the  pipes,  might  be  started  and  stopped  at  once,  and 
when  less  than  four  were  in  use  any  desired  combination  could  l)e 
made.  One  pipe  was  sounded  and  the  duration  of  audibilily  nf  llu- 
residual  soinid  determined,  of  ctmrse,  as  always  in  these  expi-ri- 
ments,  by  rei)eated  olxser  vat  ions.     The  ex[ieriment  wa,-^  then  niade 


'  Terrazzo  cement  (liK)r. 


86  REVERBERATION 

wilh  two  organ  pipes  instciid  of  one;  then  with  three  pipes;  and, 
finally,  witli  four.  The  whole  series  was  then  repeated,  but  begin- 
ninj;  with  a  different  i)ipe  and  eonibining  different  pipes  for  the  two 
and  three  pipe  sets.  In  this  way  the  series  was  repeated  four  times, 
the  combinations  being  so  made  that  each  pipe  was  given  an  equal 
weight  in  the  determination  of  the  duration  of  audibility  of  the 
residual  soiuid  under  the  four  ditl'erent  conditions.  It  is  safe  to 
assume  that  with  experiments  conducted  in  this  manner  the  average 
initial  intensities  of  the  sound  with  one,  two,  three,  and  four  pipes 
were  to  each  other  as  one,  two,  three  and  four.  The  corresponding 
durations  of  audibility  shall  be  called  /i,  U,  fs  and  /4.  The  following 
results  weri'  obtained: 

(i  =  8.69  seconds  h  -  h  =  .45  second 

/,  =  9.14       "  h-h  =  .67       " 

/,  =  9.36       "  tt-i,  =  .86       " 

U  =  9.55       " 

It  is  first  to  be  observed  that  the  difference  for  one  and  two  organ 
pipes,  .45,  is,  within  two-hundredths  of  a  second,  half  that  for  one 
and  four  organ  pipes,  .8(5.  This  suggests  that  the  difference  is 
proportional  to  the  logarithm  of  the  initial  intensity;  and  further 
inspection  shows  that  the  intermediate  result  with  three  organ 
pipes,  .67,  is  even  more  nearly,  in  fact  well  within  a  hundredth  of 
a  second,  proportional  to  the  logarithm  of  three.  This  reenforces 
the  very  natural  conception  that  however  much  the  residual  sound 
at  any  one  point  in  the  room  may  fluctuate,  passing  through  max- 
ima and  minima,  the  average  intensity  of  sound  in  the  room  dies 
away  logarithmically.  Thus,  if  one  plots  the  last  part  of  the  residual 
sound  —  that  which  remains  after  eight  seconds  have  elapsed  — 
on  the  assumption  that  the  intensity  of  the  sound  at  any  instant  is 
proportional  to  the  initial  intensity,  the  result  will  be  as  shown  in 
the  diagram.  Fig.  18.  The  point  at  which  the  diminishing  sound 
crosses  the  line  of  minimum  audibility  in  each  of  the  four  cases  is 
known,  the  corresponding  ordinates  of  the  other  curves  being 
multiples  or  submultiples  in  proportion  to  the  initial  intensity. 
The  results  are  obviously  logarithmic. 

Let  7i  be  the  average  intensity  of  the  steady  sound  in  the  room 
when  the  single  organ  pipe  is  sounding,  i  the  intensity  at  any  instant 


RATE  OF  DECAY  OF  RESIDTAL  SOUND  37 

during  the  decay,  say  t  seconds  after   the    pipe    has   ceased,  then 

di 

will  be  the  rate  of  decav  of  the  sound,  and  since  tlie  absorption 

dt  '  ' 

of  sound  is  proportional  to  the  intensity 

di 
—  —  =  Ai,    where   .1    is    the   constant    of   proportionality, 
dt 

the  ratio  of  the  rate  of  decay  of  the  residual  sound  to  the  intensity 
at  the  instant. 

—  loge  i  +  C  =  At, 

a  result  that  is  in  accord  with  the  above  experiments.  The  con- 
stant of  integration  C  may  be  determined  by  the  fact  that  when  /  is 
zero  i  is  equal  to  h;  whence 

C  =  fo(/e  /],  and  the  above  equation  becomes 
log  a  -7  =  At. 

At  tlie  instant  of  minimum  audibility  t  is  equal  to  /i,  the  wliole 
duration  of  (lie  residual  sound,  and  i  is  equal  to  i',  —  as  the  inten- 
sity of  the  least  audible  sound  will  hereafter  be  denoted.    Therefore 


We  t]  =  At 


I 


This  apiilieil  to  tlie  experiment  with  two,  three  and  four  pipes  gives 
similar  equations  of  the  form 

We  -~  =  At„, 
where  /;  is  the  number  of  organ  pipes  in  use.    By  the  elimination  of 
.,  from  tlicse  e(|uati()iis  by  i)airing  the  first  willi  lach  of  tlic  olliers, 


A 

We 

'2- 

i  _ 

tx  ~ 

1.54, 

A 

log„ 
ti- 

ti  ~ 

1.6^2, 

A 

loge 

tt- 

4  _ 

l.(il. 

-1  (average)  =  1.59, 

where  A   is  the  ratio  between  the  rate  of  decay  and  the  average 
intensity  at  any  instant. 


3S 


RKVKUHKRATIOX 


It  is  j)ossil)K'  also  ti)  tli'tcriniiic  the  initial  intensity.  It,  in  terms 
of  llie  luininiiiin  iiiulil)le  intensity,  ('. 

log^  .J  =  Ah, 

h  =  i'  logi^  Ati  =  i'  log;^  (1.59  X  8.69)  =  1,000,000  i'. 

Witli  tliis  value  of  the  initial  intensity  it  is  possible  to  calculate 
the  intensity  i  of  the  residual  sound  at  any  instant  during  the  decay, 
l.y  the  formula  %,/,-%„/  =  .K, 

and  the  result  when  plotted  is  shown  in  Figure  19,  the  unit  of  in- 
tensity being  minimum  audibility. 

A  practical  trial  early  in  tiie  year  liad  sliown  tiiat  it  would  be 
impossible  to  use  tin's  lecture-room  as  an  auditorium,  and  the  ex- 

1000,000      ;  • 


A 


900,000 

800,000 

1 
700,000 

■     1 
600,000 

l500,00( 

) 

\400,0( 

10 

\ 

300,000 

y 

\ 

200,X>00 

\lOO,00( 

) 

O 

^-J-_ 

i 

1 

2 

3       ' 

1       ! 

> 

' 

r     i 

1      9 

1 

0     1 

1     1 

2     t 

3"'l 

1     19 

Time  in  seconds 
Fio.  19.    Decay  of  sound  in  the  lecture-room  of  the  Boston  Public 
Library  beginning  immediately  after  the  cessation  of  one  organ 
pipe. 

periments  described  above,  with  others,  were  in  anticipation  of 
changes  designed  to  remedy  the  difficulty.  Hair  felt,  in  consider- 
al)le  quantities,  was  placed  on  the  rear  wall.  The  experiments  with 
the  four  organ  pipes  were  then  repeated  and  the  following  results 
were  obtained : 

/,  =  3.65  k-  h  =  M  :.  A  =  3.41 

h  =  3.85  h  ~h  =  .31  .-.  A  =  3.54 

h  =  3.96  U-h  =  .42  .-.  A  =  3.29 

/<  =  4.07 
h  =  250,000  i' 


A  =  3.41  (average) 


RATE  OF  DECAY  OF  RESIDUAL  SOUND  39 

A  few  nights  later  the  apparatus  was  moved  down  to  the  attend- 
ant's reception-room  near  the  main  entrance  —  a  small  room  but 
similar  in  i)roportions  to  tlie  lecture-room.  Here  a  careful  experi- 
ment extending  over  several  nights  was  carried  on,  and  it  gave  the 
following  results: 

U  =  4.01  t,  ~  ti  =  .19  .-.  A  =  3.65 

/2  =  4.'-20  t,  -  ti  =  .28  .-.  A  =  3.90 

/3  =  •l.'JO  ti-  li  =  .37  .-.  A  =  3.75 

U  =  4.38  A  =  3.76  (average) 

/i  =  3,800,000  i' 

The  first  interest  lies  in  an  attempt  to  connect  the  rate  of  decay, 
obtained  by  means  of  the  four  organ  pipe  experiments,  with  the 
absolute  coefficient  of  absorption  of  the  walls,  obtained  by  the 
experiments  with  the  open  and  closed  windows;  and  to  this  end 
recourse  will  be  had  to  what  shall  here  be  called  "the  mean  free 
path  betwet'u  reflec-tions."  The  residual  sound  in  its  i)rocess  of 
decay  travels  across  the  room  from  wall  to  wall,  or  ceiling,  or  floor, 
in  all  conceivable  directions;  some  paths  are  the  whole  length  of 
the  room,  some  even  longer,  from  one  corner  to  the  opposite,  but 
in  the  main  the  free  path  between  reflections  is  less,  becoming  even 
infinitesimally  small  at  an  angle  or  a  corner.  Between  the  two  or 
three  hundred  reflections  that  occur  during  its  audibility  the  residual 
sound  establishes  an  average  distance  between  reflections  that  de- 
pends merely  on  the  dimensions  of  the  room,  and  nuiy  be  called 
"its  mean  free  path." 

.171  r 

is  the  absorbing  power  of  the  room,  measured  in  open-window  units. 
Let 

«    =  surface. 

V  =  volume. 

A  =  rate  of  decay  of  tlie  soinui. 

V  =  velocity  of  sound,  '.U-^i  in.  per  second  at  20  degrees  C. 
p   =  length  of  the  mean  free  path  httweea  reflections. 

Whence      =  the  average  number  of  reflect ion>  i)er  second,  and 
P 

-   is  the  fraction  absorbed  at  each  reflection,        =  •'■ 


40 


REVEnBERATIOX 


ar       r.l71  l  .  11,1,1  *■ 

and  P  =  T  =  — r~r'    whencr  inav   be  calcuhiU'd   the  mean   tree 
,1s  .1.''  /i 

patli,  p. 


Boston  Public  Library  Lecture-room,  bare 2,140.0    1.59     1,160    8.69    7.8 

with  felt  ..  2,140.0    3.41     l.lfiO     3.0.5    8.8 
.\llentlanfs  Room 63.8    3.76        108    4.01    2.27 


The  lenpth  of  the  mean  free  path  in  the  lecture-room,  bare  or 
draped,  ouglit  to  l)e  the  same,  for  the  felt  was  placed  out  from 
the  wall  at  a  distance  imperceptibly  small  in  comparison  with  the 
dimensions  of  the  room:  l)nt  7.8  and  8.8  differ  more  than  the 
experimental  errors  justify.  Again,  the  attendant's  room  had  very 
nearly  the  same  relative  proportions  as  the  lecture-room  (about 
2  :3  -.6),  but  each  linear  dimension  reduced  in  the  ratio  3.22  :  1. 
Tiie  mean  free  path,  obviously,  should  be  in  the  same  ratio;  but 
when  the  mean  free  path  in  the  attendant's  room,  2.27,  is  multiplied 
by  3.22  it  gives  7.35,  departing  again  from  the  other  values,  7.8  and 
8.8,  more  than  experimental  errors  justify.  The  explanation  of 
this  is  to  be  found  in  the  fact  that  the  initial  intensity  of  the  sound 
in  the  rooms  for  the  determination  of  /i  was  not  the  same  but  had 
the  values  respectively,  1,000,000  i',  250,000  i'  and  3,800,000  i'. 
Since  ti  has  been  shown  proportional  to  the  logarithms  of  the  initial 
intensities,  these  three  numbers,  7.8,  8.8  and  7.35,  may  be  corrected 
in  an  obvious  manner,  and  reduced  to  the  comparable  values  they 
would  have  had  if  the  initial  intensity  had  been  the  same  in  all 
three  cases.  The  results  of  this  reduction  are  7.8,  8.0  and  8.0,  a 
satisfactory  agreement . 

The  length  of  the  mean  free  path  is,  therefore,  as  was  to  be  ex- 
pected, proportional  to  the  linear  dimensions  of  the  room,  and  such 
a  comparison  is  interesting.  There  is  no  more  reason,  however,  for 
comparing  it  with  one  dimension  than  another.  Moreover,  most 
rooms  in  regard  to  which  the  inquiry  might  be  made  are  too  irregular 
in  shape  to  admit  of  any  one  actnal  distance  being  taken  as  standard. 
Thus,  in  a  semicircular  room,  still  more  in  a  horseshoe-shaped  room 
such  as  the  common  theatre,  it  is  indeterminable  what  should  be 


RATE  OF  DECAY  f)F  RKSIDrAL  SOrXD  41 

called  the  breadth  or  what  the  length.  On  account,  therefore,  of 
the  complicated  nature  of  practical  conditions  one  is  forced  to  the 
adoption  of  an  ideal  dimension,  the  cube  root  of  liie  volume,  f  ■\  tlie 
length  of  one  side  of  a  cubical  room  of  the  same  capacity.    The  above 

data  give  as  the  ratio  of  the  value,  .62. 

It  now  becomes  possible  to  present  the  subject  by  exact  analysis, 
and  free  from  approximations;  but  before  doing  so  it  will  be  well  to 
review  from  this  new  standpoint  that  which  has  already  been  done. 

It  was  obvious  from  the  beginning,  even  in  deducing  the  hyper- 
bolic law,  that  some  account  should  be  taken  of  tiie  rethiclion  in 
the  initial  intensity  of  the  sound  as  more  and  more  absorbing 
material  was  brought  into  the  room,  even  when  the  source  of  sound 
remained  unchanged.  Thus  each  succeeding  value  of  the  duration 
of  the  residual  sound  was  less  as  more  and  more  absorbing  material 
was  brought  into  the  room,  not  merely  because  the  rate  of  decay 
w:is  greater,  but  also  because  the  initial  intensity  was  less.  Had  the 
initial  intensity  in  some  way  been  kept  up  to  the  same  value  through- 
out the  series,  the  resulting  curve  would  have  been  an  exact  liyper- 
bola.  As  it  was,  however,  the  curve  sloped  a  little  more  rapitlly  on 
account  of  the  additional  reduction  in  the  duration  arising  from  the 
reduction  in  initial  intensity  of  the  sound.  At  the  time,  there  was 
no  way  to  make  allowance  for  this.  That  it  was  a  very  small  error, 
however,  is  shown  bj'  the  fact  that  the  departures  from  the  true 
hyperbola  that  were  tabulated  are  so  small. 

Turning  now  lo  the  i)arameter,  k,  it  is  evident  lliat  this  also  was 
an  approximation,  though  a  close  one.  In  the  first  place,  iis  just 
explained,  the  experimental  curve  of  calibration  sloped  a  little  more 
rapidly  than  tlie  tr\ie  iiy])erbola.  It  follows  that  the  nearest  hyper- 
bola fitting  the  actual  experimental  results  was  always  of  a  little 
too  MiKill  parameter.  Eurtlier,  /.•  depended  iiol  uurcly  mi  llic  uni- 
formity of  the  initial  intensity  during  the  (•alil)ration  of  the  room, 
but  also  on  the  a1)solute  value  of  tliis  intensity.  Tluis,  /,•  =  ati,  ami 
ti  is  in  turn  proportional  to  llic  logarithm  of  tlic  initial  intensity. 
Therefore  in  order  to  fully  define  h  we  must  adopt  some  standard  of 
initial  intensity.     For  this  purpose  we  shall  hereafter  take  as  the 


42  RKVKHHKUATIOX 

sUindard  coiulition  in  initial  intensity,  /  =  1,000,000  i',  (/  =  10®  i'), 
wluTi-  ?■'  is  tlu-  niiniinuni  aiidihle  intensity,  as  this  is  the  nearest 
round  number  to  the  average  intensity  prevailing  during  these  ex- 
periments. If,  therefore,  during  the  preceding  experiments  the 
initial  intensity  was  above  the  standard,  the  value  deduced  for  k 
would  be  a  little  high,  if  below  standard,  a  little  low.  This  variation 
of  the  parameter.  Ic,  would  be  slight  ordinarily,  for  k  is  proportional 
to  the  logarithm,  not  directly  to  the  value  of  the  initial  intensity. 
Slight  ordinarily,  but  not  always.  Attention  was  first  directed  to 
its  practical  importance  early  in  the  whole  investigation  by  an  ex- 
periment in  the  dining-room  of  Memorial  Hall  —  a  very  large  room 
of  17,(HK)  c  iil)ic  meters  capacity.  During  some  experiments  in  Sanders 
Theatre  the  organ  pipe  was  moved  across  to  this  dining-room,  and 
an  experiment  begun.  The  reverberation  was  of  very  short  duration, 
although  it  would  have  been  long  had  the  initial  intensity  been 
standard,  for  in  rooms  constructed  of  similar  materials  the  rever- 
beration is  approximately  proportional  to  the  cube  roots  of  the 
\ohunes.  There  was  no  opportunitj'  to  carry  the  experiment  farther 
than  to  observe  the  fact  that  the  duration  was  surprisingly  short, 
for  the  frightened  apjiearance  of  the  women  from  the  sleeping- 
rooms  at  the  top  of  the  hall  put  an  end  to  the  experiment.  Finally, 
fc  is  a  function  not  merely  of  the  volume  but  also  of  the  shape  of  the 
room;  that  is  to  say,  of  the  mean  free  path,  as  has  already  been 
explained. 

It  wius  early  recognized  that  with  a  constant  source  the  average 
intensity  of  the  sound  in  different  rooms  varies  with  variations  in 
size  and  construction,  and  that  proper  allowance  should  be  made 
therefor.  The  above  results  call  renewed  attention  to  this,  and 
point  the  way.  In  the  following  paper  the  more  exact  analysis  will 
be  given  and  applied. 


EXACT  SOLUTION  43 


EXACT  SOLUTION 

The  present  paper  will  carry  forward  the  more  exact  analysis  pro- 
posed in  the  hist  i)aper. 

For  the  sake  of  reference  the  nomenclature  so  far  introduced  is 
here  tabulated. 

t  =  lime  after  the  source  has  ceased  up  to  any  instant  whatever  liuring 

the  decay  of  the  sound. 

/',  t",  t'"  =  (hiration  of  the  residual  sound,  the  accents  indicating  a  changed 

condition  in  the  room  sucii  as  tlie  intnxhiction  or  removal  of 
some  al)Sorlient,  the  presence  of  an  au<iien<'e,  or  the  opening  of 
a  window. 

h,  hi  •  ■  ■  ta  =  whole  duration  of  the  residual  .sound,  the  subscripts  indicating  the 
nnniher  of  organ  [lipes  used. 

T  =  <luration  of  the  resi<lual  sound  in  a  room  when  the  initial  intensity 

has  been  standard. 

i  =  intensity  of  the  residual  .sound  at  any  instant. 

i'  =  intensity  of  minimum  audil>ility. 

I\,  Ii,  .  .  .  I„  =  intensity  of  sound  in  the  room  just  as  the  organ  pipe  or  pipes  stop, 
the  subscripts  indicating  number  of  [)ipes. 

I  =  standard  initial  Intensity  arbitrarily  adopted,  /  =  1,000,000  i'. 

W  =  absorbing  power  of  the  oi)cn   windows,   minus   their  ab.sorlting 

power  when  closed  =  area  (1  —  .024). 

a  =  ab.sorbing  power  of  the  room. 

Oi,  02,  .  .  .  a,i  =  coefficients  of  absorption  of  the  various  components  of  the  wall- 
surface. 

S  =  area  of  wall  (and  floor)  surface  in  square  meters. 

*i,  S2,  .  .  .  *n    =  area  of  the  various  comi)onents  of  the  wall-surface. 

V  =  volume  of  the  room  in  cubic  meters. 
k  =  hyperbdlic  parameter  of  any  room. 

K  =  ratio  of  the  parameter  to  the  volume.  aT  =  k  =  KV. 

A  =  rate  of  decay  of  tlie  sound. 

p  =  length  of  mean  free  path  between  reflections. 

V  =  velocity  of  sound,  3-J'2  m.  per  second  at  20°  C. 

Let  E  denote  Die  rate  of  emission  of  energy  from  the  single 
organ  pipe. 

^  =  the  average  interval  of  time  between  reflections. 


-E  =  aiiioiiiil  of  eiiergv  eniilted  during'  tliis  iiiUrval. 

V 

^  e(i  —")   =  amount  of  energy  left  after  I  he  first  reflection. 

V  E  (\  -")   =  amount  of  energy  left  after  the  second  reflection,  etc. 


H  HKVKUnKHATIOX 

If  I  lit-  iirj,';in  pii"'  contimu-s  to  sound,  the  energy  in  the  room  con- 
timifs  to  acciiimilate,  at  first  rapidly,  afterwards  more  and  more 
slowly,  and  finally  reaches  a  practically  steady  condition.  Two 
|)oints  are  here  interesting,  —  the  time  reciuind  lor  llie  sound  to 
reach  a  practically  steady  condition  (for  in  tlie  experiments  the 
organ  pipes  ought  to  he  sounded  at  least  this  long),  aiul  second,  the 
intensity  of  the  sound  in  the  steady  and  final  contlition.  At  any 
instant,  the  total  energy  in  the  room  is  that  of  the  sound  just  issuing 
from  till'  ]>ii)e.  Mot  having  suffered  any  reflection,  plus  the  energy  of 
that  which  Inus  suffered  one  reflection,  that  which  has  suffered  two, 
that  which  has  suffered  three,  and  so  on  hack  to  that  which  first 
issueil  from  the  pipe,  as: 

where  n  is  the  number  of  reflections  suffered  by  the  sound  that  first 
issued  from  the  pipe,  and  is  equal  to  the  length  of  time  the  i)ipe  was 
blown  divided  by  the  average  interval  of  time  between  reflections. 
The  above  series,  which  is  an  ordinary  geometric  progression,  may 
be  written 

?£ )-^  :  m 


(>-:) 


is  by  nature  positive  and  less  than  unity.     If  /;  is  very  large  or  if 
is  small  this  may  be  written 

- —  =  the  total  energy  in  the  room  in  the  steadv  condition.    (2) 
va  .  V  / 

i^ = ^;  (3) 

avV  ^  ' 

is  the  average  intensity  of  soimd  in  the  room  as  the  organ  pipe 
stops.  Substituting  in  this  equation  the  values  of  a  and  p  already 
found, 

«  =  ^  '  (4) 

va       vKV 


EXACT  SOLUTION  45 

J       vKV      T      Es        E 
wehave  ^' =  Sat' KV' ^  =  M''  ^^^ 

Also 
whence 


/.  =  log?  Ah.  (7) 

/:  =  (-.f  /or/--  .1/,,  (8) 


wlitTf  the  unit  of  enorgy  is  the  energy  of  niininiuni  audibility  in  a 
cubic  meter  of  air. 

It  remains  to  determine  A'  and  a.  To  this  end  the  four  organ 
pipe  experiments  must  be  nuide  in  a  room  with  the  windows  closed 
and  with  them  open,  and  the  values  of  A'  and  A"  deternu'ned.  The 
following  analysis  then  becomes  available: 

AT         ,       ,  KV 

a  =    y,   ,  and  a  +  w  =  ^  - 

whence 

a  +  w       T  ' 

For  >lan<!aril  conditions  in  regard  to  initial  intensity 

A'  r  =  A"  T"  =  lag,  I  =  log,  (lO-^)  =  13.8, 

r       A'  ,  ^,       13.8 

j;r  =  ^.andr    =-^. 

Substituting  these  values, 


a  A'      ,.       al"       a  13.8 

:.  A  = 


a  +  w       A"'  V         A'V 

whence 


and 


•^'YW^y  « 


Or  if  A  lias  been  determined  (!))  nuiy  l)e  written 

«  =  •''>''-.  (11) 

13.8 

a  useful  form  of  the  equation. 

From  equation  (1)  and  ('■2)  we  may  calculate  the  rate  of  growth 
of  soiuid  in   tlie  room  as  it   approaches  the  final  steady  c*>ndition. 


46  KK\KUBERATION 

Thus,  dividing  (1)  by  (2),  the  result,  1  -  (l  -  ^)°,  gives  the  in- 

tt-nsitv  at  aiiv  instant  h?  seconds  after  the  sound  has  started,  in 

terms  of  the  final  steady  intensity.  Of  all  the  rooms  so  far  experi- 
mented on,  liie  growth  of  the  sound  was  slowest  in  the  lecture-room 
of  the  Boston  Public  Library  in  its  unfurnished  condition.    For  this 

room  -  =  .037,  and  p  =  8.0  meters.    The  following  table  shows  the 

growth  of  the  sound  in  this  room,  and  the  corresponding  number  of 
reflections  which  the  sound  that  first  issued  from  the  pipe  had 
undergone. 

Lecture-koom.  Boston  Public  Libhauy 


II 

Time 

Average 
Intensity 

n 

'nnw 

Average 
Intensity 

1 

.02 

.04 

30 

.69 

.08 

5 

.11 

.17 

40 

.92 

.78 

10 

.23 

.31 

50 

1.15 

.85 

15 

.84 

.43 

100 

2.30 

.98 

20 

.46 

.53 

150 

3.45 

.997 

00 


00 


1.00 


It  thus  appears  that  in  this  particular  room  the  organ  pipe  must 
sound  for  about  three  seconds  in  order  that  the  average  intensity 
of  the  sound  may  get  within  ninety-nine  per  cent  of  its  final  steady 
value.  As  throughout  this  work  we  are  concerned  only  with  the 
logarithm  of  the  initial  intensity,  ninety-nine  per  cent  of  the  steady 
condition  is  abundantly  near.  Tliis  consideration  —  the  necessary 
length  of  time  the  organ  pipe  should  sound  —  is  carefully  regarded 
throughout  these  experiments.  It  varies  from  room  to  room,  being 
greater  in  large  rooms,  and  k-ss  in  rooms  of  great  absorbing  power. 

To  determine  the  value  of  E,  the  rate  of  emission  of  sound  by 
the  pipe,  formula  (8),  E  =  VA  logP  Ah,  is  available.  It  is  here  to 
be  observed  that  as  this  involves  the  antilogarithm  of  Ati  these 
quantities  must  be  determined  with  the  greatest  possible  accuracy. 
The  first  essential  to  this  end  is  the  choice  of  an  appropriate  room. 
Without  giving  the  argument  in  detail  here,  it  leads  to  this,  that 
the  best  rooms  in  which  to  experiment  are  those  that  are  large  in 
volume  and  have  little  absorbing  power.  In  fact,  for  this  purpose, 
small  rooms  are  almost  useless,  but  the  accuracy  of  the  result  in- 


EXACT  SOLUTION  47 

creases  rapidly  with  an  increase  in  size  or  a  decrease  in  absorbing 
power.  On  this  account  the  lecture-room  of  the  Boston  Public 
Library  in  its  unfurnished  condition  was  by  far  the  best  for  this 
determination  of  all  the  available  rooms.  Inserting  the  numerical 
magnitudes  obtained  in  this  room  in  the  equation, 

E  =  VAlogl^Ati  =  2,140  X  1.59  logl' {1.59  X  8.69)  =  3,400,000,000. 

If  the  observations  in  the  same  room  after  the  introduction  of  the 
felt,  already  referred  to,  are  used  in  the  equation  the  resulting  value 
of  E  is  3,200,000,000.  The  agreement  between  the  two  is  merely 
fortunate,  for  the  second  conditions  were  very  inferior  to  the  first, 
and  but  little  reliance  should  be  placed  on  it.  In  fact,  in  both  re- 
sults the  second  figures,  4  and  2,  are  doubtful,  and  the  round  num- 
ber, 3,000,000,000,  will  be  used.    It  is  sufficiently  accurate. 

The  next  equation  of  interest  is  that  giving  the  value  of  K, 
number  (10).  It  contains  the  expression.  A"  —  A',  the  difference  be- 
tween the  rates  of  decay  with  the  windows  open  and  witli  themclosed; 
A"iind  ^1' depend  linearly  on  the  difference  in  duration  of  the  residual 
sound  with  four  organ  pipes  and  with  one,  and  jis  both  sets  of  dif- 
ferences are  at  best  small,  it  is  evident  that  these  experiments  also 
must  be  conducted  with  the  utmost  care  and  under  the  best  con- 
ditions. The  best  conditions  would  be  in  rooms  that  are  large,  that 
have  small  absorbing  power,  and  that  afford  window  area  sufficient 
to  about  double  the  absorbing  power  of  the  room.  Practically  this 
would  be  in  large  rooms  that  are  of  tile,  brick,  or  cement  walls, 
ceiling  and  floor,  and  have  an  available  window  area  equal  to  about 
one-fliirlieth  of  tlie  total  area. 

The  lobby  of  the  Fogg  Art  Museum,  although  rather  small,  best 
satisfied  the  desired  conditions.  Sixteen  organ  pipes  were  used, 
arranged  four  on  each  air  tank  and,  Micrefore,  near  together.  Thus 
arranged,  the  sixteen  i)ipes  had  7.0  times  the  intensity  of  one,  as 
detennined  by  a  subsequent  experiment  in  the  Physical  Laboratory. 
The  following  results  were  obtained: 

,   ^  tog.  7.6  ^  _Jog,l.6_  ^  3  Q 
t\t-t\       5.26-4.59 

,  Af  -       '"??  "^-^^       -   1  - 

and  A    "3.43 -3.00  "■*•'• 


48  iu;m:hhkhatk)n 

l'3.»w  1:J.8  X  1.8,5 

A  = = =  .loo. 

V(A'  -A')         96  X  1.7 

lien'.  liowfVcT,  it  is  t-iisy  to  sliow  by  trial  that  t-rrors  of  only  one- 
luiiulncllli  of  a  second  in  the  four  detorniinations  of  the  duration 
of  the  residual  sound  would,  if  additive,  give  a  total  error  of  twenty 
l)er  cent  in  tin-  result. 

It  is  iiii|)ossil)le,  es])ecially  with  open  windows,  to  time  with  an 
accuracy  of  more  than  one-Jmndredtli  of  a  second,  and,  therefore, 
this  fornmla, 

13.8«; 


A'  = 


ViA"  -  A') 


while  analytically  exact  and  attractive  in  its  simplicity,  is  practi- 
cally unserviceable  on  account  of  the  sensitive  manner  in  which  the 
observations  enter  into  the  calculations. 

The  following  analysis,  however,  results  in  an  equation  much 
more  forbidding  in  appearance,  it  is  true,  but  vastly  better  practi- 
cally, for  it  involves  the  data  of  difficult  determination  only  logarith- 
mically, and  then  only  as  part  of  a  comparatively  small  correcting 
term.  For  the  room  with  tlie  windows  closed: 
A't\  =  loy^I'u 

and  for  standard  conditions  in  regard  to  initial  intensity 
A'  r  =  log,  I, 

whence 

r    =  v,  -  :^^iogJ-^- 

T'a  =  AT, 


hence 


AT   =t'ia  -  j,log^Y'^ 


and  similar  steps  for  the  same  room  with  the  windows  open  give 
KV  =  fi  (a  -1-  it;)  -  ^--^~  loge  -j  ■ 

-Mullii)lyiiig  the  first  of    the  last  two  equations  by  t"u   and  the 
second  by  t'l, 

K  -  1  [„„/ ,,'     ,    /«'".  ,       1\       {a  +  w)t\  ,       /"A] 


EXACT  SOLUTION  49 


Bj'  equation  (5) 


a        !<p 

Z'  "  7 

and  similarly 

a  -\-  w       sp 

A"      ~   V 

Subslitiiling  these  values  in  I  he  above  equation, 


(12) 


As  an  illustration  of  the  application  of  the  last  equation,  the 
case  of  the  lobbyof  the  Fogg  Art  ^luseuni  is  here  worked  out  at 
length. 

t'l  =  4.5!) 
t'\  =  .S.OO 
F  =  96  cii.  111. 
S  =  125  sq.  111. 
w  =  1.8G 

a  =  - — ; —  =  3.58  as  a  first  approximation 

p  =  2.8 

/',  =  2^  =  8.8  X  106  i' 
vaV 

/".  =     ,    ^\,.  =  5.8  X  10«  i' 

V  (a  +  w)  V 

Substituting  these  values  in  the  above  equation, 

A'  =      —  [25.7  +  1.02  (6.53  -  8.1)1  =  .169  -  .010  =  .159, 
152 

where  the  t.eriii  .169  is  the  value  of  A'  that  would  i)e  deduced  dis- 
regarding the  initial  intensity  of  the  sound,  —  .010  is  the  correction 
for  this,  and  .15!)  is  llie  corrected  value  of  A'.  'Hie  magnitude  as 
well  as  the  sign  of  liiis  correction  dejieuds  on  the  intensity  of  the 
source  of  sound,  the  size  of  the  room  and  the  material  of  which  it 
is  constructed,  and  the  area  tif  the  windows  opened.  This  is  illus- 
trated in  llie  following  table,  which  is  derived  from  a  recalculation 
of  all  the  rooms  in  which  the  open-window  exiieriment  has  lieeii 
tried,  and  which  exliiiiils  a  fairly  large  range  in  these  respects: 


50 


REVERBERATION 


Boom 


Uncor- 
rected 


Correc- 
tion 


I^ihhy  Fojig  Museum 

Ix>lihv  Fork  Museum.  10  pipes.  . 
Jefferson  I'hysieal  I^ahoriitory  15 
Jefferson  I'liysu'iil  Lalioratory  1  . 
Jefferson  I'liysieul  Lalxirulory  41 


96 

96 

202 

1,630 

1,960 


8,800,000 

67,000,000 

1,700,000 

;!!)0,000 

300,000 


1.86 
1.86 
5.10 
12.0 
14.6 


.169 
.191 
.164 
.150 
.137 


-.010 
-.027 
-f.005 
+  .017 
-f.024 


.159 
.164 
.169 
.167 
.161 


Average  value  oi  K  =  .164 


Tlic  value,  A'  =  .164,  having  been  adopted,  interest  next  turns 
to  the  determination  of  tlie  ab.sorbing  power,  a,  of  a  room.  For  this 
purpose  we  have  clioice  of  three  equations,  two  of  which  have 
already  been  deduced,  (9)  and  (11), 


a  = 


A'w 
r  -  A' 


and 


A'KV 
13.8 


and  a  third  equation  may  be  obtained  as  follows: 
It  has  been  shown  that 


and 

Therefore 

and 


r  =  (',  -  '^  log 
va 


T'a  =  KV. 


I\ 


ai\  -  "£  log,  ^-^  =  KV, 


a  =  l{KV  +  ^flog.^) 


(13) 


Of  these  three  equations  the  first,  (9),  for  reasons  already  pointed 
out  in  regard  to  a  similar  equation  for  A',  while  rigorously  correct, 
yields  a  result  of  great  uncertainty  on  account  of  its  sensitiveness 
to  slight  errors  in  the  several  determinations  of  the  duration  of  the 
residual  sound.  The  second,  (11),  is  very  much  better  than  the 
first,  but  stDl  not  satisfactory  in  this  respect.  The  third,  (13),  is 
wholly  satisfactory.     It  has  the  same  percentage  accuracy  as  t'l. 


EXACT  SOLUTION  51 

and  the  only  elements  of  difficult  determination  enter  logarithmi- 
cally in  a  small  correcting  term. 

As  an  illustration  of  the  application  of  these  equations  we  maj' 
again  cite  the  case  of  the  lobby  of  the  Fogg  Art  Museum: 

,  ,.        ,„.  3.0  X  1.86      „„ 

by  equation    (9),  a  =  ^     ^     ^    =3.3; 

k             f       /^l^            3.0  X  .164  X  06       „^ 
by  equation  (11),  a  =  —-- =  3.4; 

by  equation  (13),  a  =  ~  (.164  X  96  +  1.02  X  log„  8.8)  =  3.8. 
4.59 

The  first  two  are  approximate  only,  the  last,  3.8,  is  correct,  with 

certainty  in  regard  to  the  last  figure. 

There  is  but  one  other  subject  demanding  consideration  in  this 
way,  —  the  calculation  of  the  absorbing  jiower  of  object-s  lirought 
into  the  room,  as  cushions,  drapery,  chairs,  and  other  furniture. 
This  may  be  approached  in  two  ways,  either  by  means  of  the  rate 
of  decay  of  the  sound  and  the  four  organ  pipe  experiment,  or  by 
open-window  caliliration  and  a  single  organ  i)ipe. 

Let  A'"  be  the  rate  of  decay  when  the  object  is  in  the  room,  .1' 
being  the  rate  when  the  room  is  emiity.  Then  if  a'  is  the  absorbing 
power  of  the  object : 

A'KV 


a  = 


and 


Whence 


a -[-a' 


13.8 

A'"  KV 


13.8 


«'  =  (^"'--^'^i^-  (u) 


Or  from  I  lie  other  point  of  view,  f(|ii;iti()ii  (13), 

«  =  ^,   ( A'  I  ■  +  —  log„  -  - 
/'i  \  V  I 


whence 


—7.7^ 7  U '"''  1  -  P;  '"''•  ^i)  •  (15) 


52  REVERBERATION 

where  I\  and  I"\  are  to  be  calculated  as  heretofore  by  a  preliminary 
and  approximate  estimate  of  a  and  a  . 

Here  also  it  is  easy  to  show  a  priori  that  the  first  equation,  (U), 
while  perfectly  correct  and  analytically  rigorous,  is  excessively 
sensitive  to  verj'  slight  errors  of  observation,  and  that  on  this  ac- 
count equation  (15)  is  decidedly  preferable.  For  example,  felt 
being  I)r()iight  into  the  lobby  of  the  Fogg  Lecture-room  and  placed 
on  the  floor,  the  values  of  A'"  and  t"\  were  determined  to  be,  re- 
spectively, 4.9  and  2.79.  Borrowing  from  the  preceding  experiment, 
and  substituting  in  equations  (14)  and  (15)  we  have 

„.=  («- 3.0)  •'«t,f"=«. 

,       .164x96(4.59-2.70)       ,»,/!,       qo  ^     i       r  ^\       o  j. 

a    = ^^ —  1.0"2  I  /of/e8.8  —  /r»(7efi-l  )  =  2.4, 

4.59X2.79  \4.59    •"  2.7!)     ''       / 

a  very  satisfactory  agreement  in  view  of  the  extreme  sensitiveness 
of  equation  (14). 

Thus  three  equations  have  been  deduced,  number  (12)  for  the 
calculation  of  the  parameter,  k,  (13)  for  the  absorbing  power,  a,  of 
the  wall-surface,  and  (15)  for  the  absorbing  power,  a',  of  introduced 
material.  Each  has  been  verified  by  other  equations  analytically 
rigorous,  and  developed  along  very  different  lines  of  attack.  In 
each  case  the  agreement  was  satisfactory,  especially  in  view  of  the 
extreme  sensitiveness  of  the  equations  used  as  checks. 

In  the  succeeding  paper  will  be  deduced,  by  the  method  thus 
established,  the  coefficients  of  absorption  of  the  materials  that  are 
used  ordinarily  in  the  construction  and  furnishing  of  an  auditoi'ium. 


THE  ABSORBING  POWER  OF  AN  AUDIENCE, 
AND  OTHER  DATA 

Ix  this  paper  will  be  given  all  the  data  ordinarily  necessary  in 
calculating  the  reverberation  in  any  auditorium  from  its  plans  and 
specifications.  In  order  lo  show  the  degree  of  confidence  to  which 
these  data  are  entitled  a  very  brief  account  will  be  given  of  the 
experiments  by  means  of  which  they  were  obtained.  Such  an  ac- 
count is  especially  necessarj'  in  the  case  of  the  determmation  of  the 
absorbing  power  of  an  audience.    This  coefficient  is,  in  the  nature 


ABSORBING  POWER  OF  AX  AFDIEXCE  53 

of  things,  a  factor  of  every  problem,  and  in  a  majority  of  cases  it  is 
one  of  the  most  important  factors;  yet  it  can  be  determined  only 
through  the  courtesy  of  a  large  number  of  persons,  and  even  then 
is  attended  with  difficulty. 

The  formulas  that  will  be  used  for  the  calculation  of  absorbing 
power  are  numbers  (13)  and  (15)  in  the  preceding  paper,  the  correct- 
ing terms  being  at  times  of  consideral)le  importance.  Tlie  applica- 
tion of  these  formulas  having  been  illustrated,  the  whole  discussion 
here  will  be  devoted  to  the  conditions  of  the  experiments  and  the 
results  obtained. 

In  every  experiment  the  unavoidable  presence  of  the  ol)scrver 
increases  the  absorl)ing  power.  In  small  rooms,  and  in  large  rooms 
if  bare  of  furniture,  the  relative  increase  is  considerable,  and  should 
always  be  subtracted  from  the  immediate  results  of  the  ex-periment 
in  order  to  determine  the  absorbing  power  of  the  room  alont>.  The 
quantity  to  be  sul)tracfed  is  constant,  j)roviile(l  the  same  clot  lies 
are  always  worn,  and  may  be  determined  once  for  all.  For  this 
determination  another  observer  made  a  set  of  experiments  in  a  Muall 
and  otherwise  empty  room  before  and  after  the  writer  had  entered 
with  a  duplicate  set  of  apparatus,  —  air  tank,  chronograph,  and 
battery.  In  fact,  two  persons  made  indejiendent  observations, 
giving  consistent  1,\-  tlie  result  that  the  writer,  in  the  clothes  and 
with  the  api)aratus  constantly  employed,  had  an  absorbing  power 
of  .48  of  a  imit.  For  the  sake  of  brevity  no  further  mention  will  be 
made  of  this,  but  throughout  the  work  this  correction  is  applied 
wherever  necessary. 

In  the  second  paper  of  lliis  series  a  i)r('liiuinary  calculation  was 
made  of  the  absorbing  ])()wcr  of  certain  wall-.surfaces,  ami  I  lie  ()l)jcct 
in  so  doing  was  to  gel  an  a])])roximate  value  for  the  absorbing  power 
of  glass.  It  had  been  decided  that  the  most  convenient  unit  of 
absorbing  jxiwcr  was  a  sqoiire  meter  of  open  window.  It  is  <\  idcnt, 
however,  that  the  process  of  oi)ening  a  window  during  the  progress 
of  an  experiment  is  merely  sultstitutiug  tlie  absorbing  power  of  the 
open  window  for  thai  of  the  same  window  closed,  —  a  consitleralion 
of  possililc  iiioiiiciil  ill  I  he  nicer  d<'\<'I(>pnicnl  of  I  hi-  >ul>jfcl.  1  liis 
preliminary  calculation  wa->  in  anticipation  of  and  preparation  for 
the  more  close  analysis  in  llir  fiflli  pa|>ir.     If  tlicse  cocflicients  are 


54  RKVKHBKRATIOX 

now  calculated,  using  the  corrected  formulas  of  the  fifth  paper,  we 
arrivf  at  llu-  following  results:  Cement,  and  brick  set  in  cement, 
.(h».'>,  ^'la>s.  .(►•27  and  wood  sheathing,  .061. 

TIk-  experinients  in  the  Boston  Public  Library  gave  results  that 
ju-e  interesting  from  several  points  of  view.  The  total  absorbing 
power  of  the  large  lecture-room  was  found  to  be  38.9  units  dis- 
tributed :us  follows:  A  platform  of  pine  sheathing,  exposing  a  total 
area  of  70  squjire  meters,  had  an  absorbing  power  of  70  X  .001=4.3; 
7(2  square  meters  of  glass  windows  had  an  absorbing  power  of 
7-2  X  .0*27  =  1.9;  three  large  oil  paintings,  with  a  total  area  of  17.4 
square  meters,  had  an  absorbing  jjower  of  17.4  X  .'iS  =  4.9;  the 
remainder,  "27.8  units,  was  that  of  the  cement  floor,  tile  ceiling,  and 
phuster  on  tile  walls,  in  total  area  1,095  square  meters.  This  gives 
as  the  coefficient  of  absorption  for  such  construction  .0254.  A 
similar  calculation  of  results  obtained  in  the  attendant's  room  in 
the  same  building  —  a  room  in  which  the  construction  of  the  floor, 
walls,  and  ceiling  is  similar  to  that  in  the  lecture-room  — gives  for 
the  value  of  the  coeflScient,  .0255.  The  very  close  agreement  of 
these  results,  and  their  agreement  witli  tlie  coefficient,  .0251,  for 
cement  floor  and  solid  walls  of  brick  set  in  cement  in  the  constant- 
temperature  room,  is  satisfactory.  However,  a  far  more  interest- 
ing consideration  is  the  following: 

Heretofore  in  the  argument  it  has  been  assumed,  tacitly,  that 
the  total  absorption  of  sound  in  a  room  is  due  to  the  walls,  furniture 
and  audience.  There  is  one  other  possible  absorbent,  and  only  one 
—  the  viscosity  of  the  vibrating  air.  It  is  now  i>ossible  to  present 
the  argument  that  led  to  the  conclusion  that  this,  the  viscosity  of 
the  air  throughout  the  body  of  the  room,  is  entirely  negligible  in 
comparison  with  the  other  sources  of  absorption.  These  two  rooms 
in  the  Boston  Public  Library  —  the  lecture-room  and  the  attend- 
ant's room  —  had,  in  their  bare  and  unfurnished  condition,  less 
absorbing  power  in  the  walls  than  any  other  rooms  of  their  size  yet 
found.  Therefore,  if  the  viscosity  of  the  air  is  a  practical  factor  it 
ought  to  have  shown  in  these  two  rooms  if  ever.  Fortunately,  also, 
the  two  rooms  differed  greatly  in  size,  the  volume  of  one  being  about 
thirty-five  times  that  of  the  other,  while  the  ratio  of  the  areas  of 
the  wall-surfaces  was  about  twelve.     That  part  of  the  absorption 


ABSORBINCJ  POWER  OF  AN  AUDIENCE  55 

due  to  the  walls  \vtu>  proportional  to  the  areas  of  the  walls,  and  the 
part  due  to  the  viscosity  of  the  air  was  proportional  to  the  volumes 
of  the  rooms.  As  a  matter  of  fact  the  experiments  in  these  two 
rooms  showed  that  the  whole  absorbing  power  was  accurately  pro- 
portional to  the  areas  of  the  walls;  how  accurately  is  abundantly 
e\itienced  by  the  agreement  of  the  two  coefficients,  .0^254  and  AHoa, 
deduced  on  the  supposition  that  the  viscosity  of  the  air  was  negli- 
gible. To  express  it  more  precisely,  had  the  viscosity  of  the  air 
been  sufficient  to  produce  one-fiftieth  part  of  the  absorption  in  the 
attendant's  room,  these  two  coetlicients  would  have  differed  from 
each  other  by  four  per  cent,  an  easily  measurable  amount.  It  is  safe 
to  conclude  that  in  rooms  as  bare  and  nonabsorbent  as  these  the 
viscosity  of  the  air  is  inconsiderable,  and  that  in  a  room  filled  with 
an  audience  it  is  certainly  wholly  negligible.  Rooms  more  suitable 
for  the  demonstration  of  this  ])oint  than  these  two  rooms  in  the 
Boston  Public  Library  could  hardly  be  designed,  and  access  to  them 
was  good  fortune  in  settling  so  directly  and  conclusively  this  funda- 
mental ((uestion. 

The  experiments  to  determine  the  ul)sorbing  power  of  plastered 
walls  show  it  to  be  variable.  If  the  plaster  is  applied  directly  to 
tile  or  luick  the  absorbing  power  of  the  resulting  solid  wall  is  uni- 
formly .0'25.  But  if  the  plaster  is  ai)i)lied  to  lath  held  out  from  the 
solid  wail  by  studding,  the  absorbing  i)ower  is  not  nearly  so  constant, 
varying  in  difiVrent  rooms.  The  investigation  of  this  has  not  been 
carried  far  enough  to  show  witli  absolute  certainty  the  cause,  al- 
though it  probabh'  arises  from  the  different  thickness  in  which  the 
l)laster  is  applied.  For  the  examination  of  this  point  two  modes  of 
procedure  are  ])ossible,  —  experimenting  in  a  large  number  of 
rooms,  or  experimenting  in  one  room  and  replastering  in  many 
different  ways.  The  objection  to  the  first  nietliod,  which  appears 
the  more  available,  is  that  it  is  almost  imi)ossible  to  get  accurate 
information  in  regard  to  the  nature  of  a  wall  unless  one  hivs  comjilete 
cuiilrol  of  tiie  construction.  However,  there  are  probably  interest- 
ing variations  that  cannot  be  found  in  u>f,  l)ut  that,  if  tried,  would 
be  fruitful  in  suggestions  for  future  conslruclion.  The  second 
method  -  experimenting  in  one  room,  ])lastering  and  replastering 
it  with  svslemalic  variations  antl  careful  analysis  of  the  construction 


56  RK\KI?I?l-:RA'ri()\ 

in  oacli  ciise  —  would  be  the  most  instructive,  but  the  expense  of 
such  proccihirc  is,  for  the  time  bcin^'  at  least,  prohibitive.  Ainon^ 
the  interesting  possibilities,  of  which  it  can  only  be  said  that  the 
experiments  so  fur  point  that  way,  is  that  with  time  the  plastered 
walls  improve  in  absorbing  power;  how  rapidly  has  not  been  shown, 
'lln's  change  can  be  due,  of  course,  only  to  some  real  cliange  in  the 
nature  of  the  wall,  and  the  most  probable  change  would  l>e  its  grad- 
ual drying  out.  Experiments  in  four  rooms  with  plaster  on  wood 
lath  gave  as  the  average  absorbing  power  per  scpiare  meter  .034  of 
a  unit.  Experiments  in  eight  rooms  with  plaster  on  wire  lath  gave 
as  the  average  coefficient  of  a!)sorption  .0.'5.'3.  In  both  cases  the 
variation  among  the  tliH'erent  rooms  was  such  that  the  figure  in  the 
third  decimal  place  may  be  greater  or  less  by  three,  possibly,  though 
not  probabl\".  l)y  more.  The  fact  that  a  considerable  pari  of  tlie 
wall-surface  of  several  of  the  rooms  was  of  uncertain  construction 
is  partly  responsible  for  this  uncertainty  in  regard  to  the  coefficient. 
For  the  sake  of  easy  reference  and  comparison  the.se  results  are 
tabulated,  the  unit  being  the  absorbing  power  of  a  square  meter  of 
open-window  area. 

Absorbing  Power  of  Wall-Surfaces 

Open  window 1.000 

Wood-shoatliing  (hard  pine) 061 

riastiT  on  wood  iatli 034 

Piaster  on  wire  latii 033 

(ilass,  siiifile  ihiekness 027 

I'iaster  on  tile 025 

Brick  set  in  Pcirllaml  icmcnl 025 

Next  in  interest  to  the  al)sorbing  ])ower  of  wall-surfaces  is  that 
of  an  audience.  During  the  smnmer  of  1897,  at  the  close  of  a  lecture 
in  the  Fogg  Art  Museum,  the  duration  of  the  residual  soimd  was 
determined  l)efore  and  innnediately  after  the  audience  left.  The 
patience  of  the  audience  and  the  silence  preserved  left  nothing  to 
be  desired  in  this  direction,  but  a  slight  rain  falling  on  the  roof 
.seriously  interfered  with  the  observations.  Nevertheless,  the  result, 
.87  per  jjcrson,  is  worthy  of  record.  The  experiment  was  tried  again 
in  the  summer  of  1899,  on  a  much  more  elaborate  scale  and  under 
the  most  favorable  conditions,  in  the  large  lecture-room  of  the 
Jefiferson  Physical  Laboratory.    In  order  to  get  as  much  data  and 


ABSORBING  POWER  OF  AX  AUDIENCE 


ot 


from  ;is  iiuk'perKk'nl  sources  as  possil)It',  tliree  chrom'^riij)lis  were 
ek'clrifully  connected  willi  each  other  and  with  the  electro-pneu- 
matic valve  controUing  the  air  supply  of  the  organ  pipe.  One 
chronograph  was  on  the  Icclurc-lalilc,  and  the  others  were  on  op- 
posite sides  in  the  rear  of  the  hall.  The  one  on  the  table  was  in 
charge  of  the  writer,  who  also  controlled  the  key  turning  on  and  ott" 
the  current  at  the  foiu"  instnunenls.  The  two  other  chnjuographs 
were  in  charge  of  ullicr  ohservers.  ])r()visi()n  heing  thus  made  for 
three  independent  determinations.  After  a  test  had  been  made  of 
the  absorbing  jjower  of  the  whole  audience —  157  women  and  i;?5 
men,  sufficient  to  crowd  the  lecture-room  —  one-half,  by  request, 
passed  out,  63  women  and  79  men  remaining,  and  observations 
were  again  made.  On  the  following  night  the  lecture  was  repeated 
and  ol)servations  were  again  taken,  there  lieing  present  95  women 
and  13  men.  There  were  thus  six  independent  determinations  on 
three  different  audiences,  and  by  three  observers.  In  the  following 
table  I  he  lirsl  cohiiiui  ol'  figures  gi\-('s  the  t(jlal  absorbing  ])ower  of 
the  audience  present;  the  second  gives  the  absorbing  jjower  pw 
person;  the  initials  indicate  the  observer. 


Observer 

Total  Absorbing 
Power 

.\hsorbinK  Power 
iwr  Person 

First  night 

whole  aud 

ience 

w.  c.  s. 

H.S.O 

.42 

u             u 

" 

u 

G.  LcC. 

113.0 

.39 

u           u 

half 

u 

W.  C.  S. 

58.3 

.41 

u           a 

U 

u 

G.  LeC. 

58.3 

.41 

Scc(  111(1  " 

wliolo 

u 

W.  C.  S. 

(>(>.'> 

.40 

"            '* 

E.  D.  D. 

()+.(i 

.39 

.40  (3) 

In  view  of  the  (lillicullies  of  the  e\i)eiiiiu  ut  the  consistency  of  the 
detertninatinn  is  gratifying.  'I'lie  average  result  of  I  he  ■^i\  (iil.inii- 
nalions  is  ])robai)ly  correct  williiu  two  per  cent. 

Il  is  to  be  nt)ted,  lK)we\i'r,  that  this  value,  .Kt,  is  the  ditfiieni-e 
between  the  absorbing  jjower  of  the  person  and  the  al)sorbing  power 
of  t  he  settee  and  floor  which,  when  tli<'  audience  left  the  room,  look 
ils  i)lace  as  an  absorbent.  1 1  is  evident  tiial  the  experiments  de- 
lerniincd   I  he  difference  between  the  two,  while  in  subse(|uent   cal- 


58  RKVKHin-:i{ATI()N 

culalions  we  shall  be  concerned  with  the  absohite  absorl)ing  power 
of  the  audience.  'I'o  (K-terniine  this,  on  a  following  night  all  the 
settees  were  carried  out  of  the  room,  observations  being  taken  be- 
fore and  after  the  change.  From  llu-  dala  lliiis  obtained  the  absorb- 
ing power  of  each  settee  accommodating  five  persons  was  found  to 
be  .0;}!).  or  for  a  single  seat  .0077.  Of  necessity  the  floor  still  re- 
mained, i)ut  from  a  knowledge  of  its  construction  the  absorbing 
power  of  as  much  of  the  floor  as  is  covered  by  one  person  was  cal- 
culated to  be  .0.30.  Adding  these  together  we  get  as  the  absorbing 
power  of  an  audience,  seated  with  moderate  compactness,  .44  per 
person. 

In  some  subsequent  work  it  will  be  necessary  to  know  the  ab- 
sorbing power  of  an  audience,  not  per  person,  but  per  square  meter, 
the  audience  being  regarded  broadly  as  one  of  the  bounding  sur- 
faces of  the  room.  As  each  person  occupied  on  an  average  .40  of  a 
square  meter  of  floor  area,  it  is  evident  that  the  absorbing  power 
per  square  meter  was  .96  of  a  unit. 

Under  certain  circumstances  the  audience  will  not  be  compactly 
seated,  but  will  be  scattered  about  the  room  and  more  or  less  isolated, 
for  example,  in  a  council-room,  or  in  a  private  music-room,  and  it  is 
evident  that  under  these  conditions  the  individual  will  expose  a 
greater  surface  to  the  room  and  his  absorbing  power  will  be  greater. 
It  is  a  matter  of  the  greatest  ease  to  distinguish  between  men  and 
women  coming  into  a  small  room,  or  even  between  different  men. 
In  fact,  early  in  the  investigation,  two  months"  work  —  over  three 
thousand  observations  —  had  to  be  discarded  because  of  failure  to 
record  the  kind  of  clothing  worn  by  the  observer.  The  coefficients 
given  in  the  following  table  are  averages  for  three  women  and  for 
seven  men,  and  were  deduced  from  experiments  in  the  constant- 
temperature  room. 

Absorbing  Power  of  an  Audience 

Audience  per  square  meter 96 

.\udience  per  person 44 

Isolated  woman 54 

Isolated  man 48 

"When  an  audience  fills  the  hall  one  is  but  little  concerned  with 
the  nature  of  the  chairs  —  acoustically,  but  otherwise  this  becomes 


ABSORBING  POWER  OF  AN  AUDIENCE  59 

a  matter  of  considerable  inij)ortanoe.  The  settees  in  the  lecture- 
room  of  the  Physical  Laboratory,  already  mentioned,  are  of  plain 
ash,  and  have  solid  seats,  and  vertical  ribs  in  the  back;  they  are 
without  upholstering;  and  it  is  interesting,  in  order  to  note  the 
agreement,  to  compare  the  absorbing  power  of  such  settees  per  single 
seat,  .0077,  with  that  of  the  "bent  wood"  chairs  in  the  Boston 
Public  Library,  .0082,  which  are  of  similar  character.  In  contrast 
may  be  placed  the  chairs  and  settees  in  the  faculty-room,  which 
have  cushions  of  hair  covered  with  leather  on  seat  and  back.  In 
the  same  table  will  be  entered  the  absorbing  power  of  Sanders 
Theatre  cushions,  which  are  of  hair  covered  with  canvas  and  light 
damask,  and  of  elastic-felt  cushions  —  cotton  covered  with  corduroy. 

Absorbing  Power  of  Settees,  Chairs,  axd  Ccshions 

Plain  ash  settees 039 

"       "        "       per  single  seat 0077 

"       "    chairs  "bent  wood" OOSi 

Upholstered  settees,  hair  and  leather 1.10 

"  "  per  single  seat 28 

"  {-hairs  similar  in  style 30 

Hair  cusliions  per  seat 21 

Elastic-felt  cushions  per  seat 20 

A  case  has  arisen  evin  in  the  present  paper  where  it  is  necessary 
to  know  the  absorbing  power  of  paintings  on  canvas,  and  the  ques- 
tion may  not  infrequently  arise  as  to  how  much  service  is  secured 
—  or  injury  incurred  —  acoustically  by  their  use  in  particular 
rooms.  The  oil  paintings  in  the  faculty-room,  10  in  number,  with 
a  total  area,  19.9  square  meters,  gave  opportunity  for  the  determi- 
nation of  the  desired  coefficient;  but  a  question  arises  in  regard  to 
the  method  of  reckoning  the  area.  Thus,  different  coefficients  are 
obtained  according  as  one  measures  the  canvas  only,  or  includes 
the  frames.  The  latter  method,  on  the  whole,  seems  best,  althougii 
most  of  the  absori)ti()n  is  probably  by  tlic  canviis. 

The  coefficient  for  house  plants,  which  may  be  of  piissing.  and 
possibly  practical,  interest,  was  even  harder  to  express.  A  green- 
hou.se,  140  cul)ic  iiulers  in  volunu-,  and  in  whicii  plants  occupied 
about  one-quarter  of  the  space,  showed  an  al)sorbing  jiower  greater 
lliaii  that  due  to  the  walls  and  floor  by  4  units,  or  .11  per  cubic 
meter  of  plants.     It    would  l>e  of  greater  value  to  dcterinine  the 


eO  HKVKRBKUATIOX 

ahsorhinp  power  of  such  plants  as  arc  used,  often  very  extensively, 
in  (lecorafiiig  on  festival  occasions,  hut  no  opportunity  lias  yet 
pres«-iit(il  itself. 

Ainonj;  the  cloths  used  in  decorations,  cheesecloth  and  cretonne 
may  l)e  taken  as  types.  The  first  is  an  American  Rauze.  48  grams 
to  the  s<|uare  meter.  The  second  is  an  ordinary  cotton-jjrint  cloth, 
184  frrams  |)er  stjuare  meter.  Shelia.  an  extra  quality  of  chenille, 
is  a  regular  curtain  material  used  only  in  ])ermanent  decorations. 

Linolciiiii  and  cork  are  commercial  products,  the  first  used  as 
floor  covering  and  the  .second  in  walls,  liotli  were  tested  lying 
l<K>seIy  on  the  floor;  cemented  in  place,  their  values  would  probably 
he  different. 

The  carijct  rug  is  a  heavy  pile  carpet  about  .8  centimeter  thick. 

In  the  following  table  the  values  are  per  square  meter,  except  in 
the  case  of  plants,  where  the  coefficient  is  per  cubic  meter: 

Miscellaneous 

Oil  paintings,  inclusive  of  frames 28 

House  planls 11 

Carpet  rugs 20 

Oriental  rugs,  extra  heavy 29 

Ciieesecloth 019 

Cretonne  eloth 15 

Slielia  curtains 23 

Hairfelt,  '-'..5  em.  tliiek.  8  cm.  from  wall 78 

Cork,  •i.o  em.  thick,  loose  on  floor 16 

Linoleimi,  loose  on  floor 12 


(  AL(  ILATION  IN  ADVANCE  OF  CONSTRUCTIOX 

In  the  present  paper  it  is  the  purpose  to  show  the  application  of 
the  preceding  analysis  and  data,  taking  as  an  exani]jle  the  design 
of  the  new  Boston  Music  Hall'  now  under  construction,  Messrs. 
McKini.  Mt  ad  &  White,  architects. 

In  the  introductory  pai)er  the  general  i)rol)lem  of  architectural 
acoustics  was  shown  to  be  a  fairly  comiilicated  one,  and  to  involve 
in  its  solution  considerations  of  loudness,  of  interference,  of  reso- 
nance, and  of  reverberation.  All  these  points  received  considera- 
tion while  the  Hall  was  being  designed,  but  it  is  proposed  to  discuss 

'  Huston  Sympliony  Hall. 


CALCULATION  IN  CONSTRUCTION       61 

here  only  the  case  of  reverberation.  In  this  respect  a  ninsic  hall  is 
peculiarly  interesting.  In  a  theatre  for  dramatic  performances, 
where  the  music  is  of  entirely  subordinate  importance,  it  is  desirable 
to  reduce  the  reverberation  to  the  lowest  possible  value  in  all  ways 
not  inimical  to  loudness;  but  in  a  music  hall,  concert  room,  or 
opera  house,  this  is  (Iccidcdiy  not  the  case.  To  reduce  the  rever- 
beration in  a  hall  to  a  niiniiiuiiii.  or  lo  make  the  conditions  such  that 
it  is  very  great,  may,  in  (■cilain  ca.ses,  present  [jractical  difficulties 
to  the  architect  —  the()reticall\-  it  presents  none.  To  adjust,  in 
original  design,  the  reverberation  of  a  hall  to  a  particular  and  ap- 
proved value  refiuires  a  study  of  conditions,  of  materials,  and  of 
arrangement,  for  wliicli  it  has  been  tlie  object  of  tlie  preceding 
l>ai)ers  to  prepare. 

It  is  not  at  all  difficult  to  show  a  priori  that  in  a  liall  for  orches- 
tral nuisic  the  reverberation  siiould  neither  be  very  great,  nor,  on 
the  oliitT  hand,  cxtremi'ly  small.  However,  in  this  matti-r  it  was 
not  necessary  to  rely  on  theoretical  considerations.  Mr.  Gericke, 
the  conductoi-  of  ilic  Boston  Syni|)ii()n\-  Orchestra,  made  the  state- 
ment that  an  orclicstra,  meaning  b_\-  this  a  symphony  orchestra,  is 
never  heard  to  tiie  best  advantage  in  a  theatre,  that  the  sound 
seems  o])pressed,  and  thai  a  ccrlaiii  amount  of  rcNcrberation  is 
necessary.  An  examination  of  all  the  availal)le  plans  of  the  halls 
cited  as  more  or  less  satisfactory  models,  in  the  preliminary  dis- 
cussion of  the  plans  for  the  new  hall,  showi'd  that  they  were  such 
as  to  give  greater  re\('rberati()n  than  tiie  ordinary  theatre  style  of 
construction.  While  several  jjlans  were  thus  cursorily  i-xamined 
the  real  discussion  was  based  on  only  two  buildings  —  the  i)resen! 
Boston  Music  Ilall  and  tlu-  Leipzig  (iewantlhaus;  one  was  familiar 
to  all  and  inunediately  accessible,  the  other  familiar  to  a  mmilur-  of 
those  in  consullal  i<in,  and  iK  |ilan>  m  grcal  dcl.-nl  were  to  lie 
found  ill  Iht.'i  ucuc  (icu'duillidus  m  Lajriij.  ran  I'liiil  linipiiis  innl  II . 
Srlnnicdcn.  It  should,  pcrliai)s,  lie  immedialely  added  that  iicillier 
hall  served  as  a  modi!  arcliitecturall.w  but  that  i)olh  were  u>ed 
rather  as  defiiiilions  and  starting  puiul-.  dii  llic  a(()U-~l  ical  xide  of 
the  di.scu.ssion.  The  old  Music  Ilall  wa--  no!  a  desirable  model  in 
e\'ery  respect,  even  acoiislically.  and  tlic  l,<ipzig  (lewaiidliaiis. 
having  a  sealing  capacity   al)out    that    of    Sanders   'I'heatre,    IJUO, 


(5^2  UKVKIUJKKATION 

was  so  small  lus  to  he  debarred  from  serving  directly,  for  this  if  for 
no  other  reason. 

The  history  of  tlie  new  hall  is  about  as  follows:  A  number  of 
years  ago.  when  the  subject  wiis  first  agitated,  Mr.  McKim  prepared 
plans  and  a  model  along  classical  lines  of  a  most  attractive  audi- 
toriuni.  and  afterwards,  at  Mr.  Iligginson's  instance,  visited 
Europe  for  the  i)urpose  of  consulting  with  nnisical  and  scientific 
authorities  in  France  and  Germany.  But  the  Greek  Theatre  as  a 
music  hall  was  an  untried  experiment,  and  l)ecause  untried  was  re- 
garded as  of  uncertain  merits  for  the  purjwse  by  the  conductors 
consulted  by  Mr.  Iligginson  and  Mr.  McKim.  It  was,  therefore, 
abandoned.  Ten  years  later,  when  the  project  was  again  revived, 
the  conventional  rectangular  form  was  adopted,  and  the  intention 
of  the  building  connnittee  was  to  follow  the  general  proportions  and 
arrangement  of  the  Ix'ijjzig  Gewandhaus,  .so  enlarged  as  to  increase 
its  seating  capacity  about  seventy  per  cent;  thus  making  it  a  little 
more  than  equal  to  the  old  hall.  At  this  stage  calculation  was  first 
applied. 

The  often-repeated  statement  that  a  copy  of  an  auditorium 
does  not  necessarily  possess  the  same  acoustical  qualities  is  not 
justified,  and  invests  the  subject  with  an  unwarranted  mysticism. 
The  fact  is  that  exact  copies  have  rarely  been  made,  and  can  hardly 
be  expected.  The  constant  changes  and  improvements  in  the  ma- 
terials used  for  interior  construction  in  the  line  of  better  fireproofing 
—  wire  lath  or  the  ai)i)lication  of  the  plaster  directly  to  tile  walls  — 
have  led  to  the  taking  of  liberties  in  what  were  perhaps  regarded  as 
nonessentials;  this  has  resulted,  as  shown  by  the  tables,  in  a 
changed  absorbing  power  of  the  walls.  Our  increasing  demands 
in  regard  to  heat  and  ventilation,  the  restriction  on  the  dimensions 
enforced  by  location,  the  changes  in  size  imposed  by  the  demands 
for  seating  capacity,  have  prevented,  in  different  degrees,  copies 
from  being  cojjies,  and  models  from  successfully  serving  as  models. 
So  different  have  been  the  results  under  what  was  thought  to  be 
safe  guidance  —  but  a  guidance  imperfectly  followed  —  that  the 
belief  has  become  current  that  the  whole  subject  is  beyond  control. 
Had  the  new  Music  Hall  been  enlarged  from  the  Leipzig  Gewandhaus 
to  increase  the  seating  capacity  seventy  per  cent,  which,  proportions 
being  preserved,  would  have  doubled  the  volume,  and  then  built,  as 


CALCn.ATION  IN  CONSTRUCTION  GS 

it  is  being  built,  according  to  the  most  modern  methods  of  fireproof 
construction,  the  result,  unfortunately,  would  have  been  to  con- 
firm the  belief.  No  mistake  is  more  easy  to  make  than  that  of 
copying  an  auditorium  —  but  in  different  materials  or  on  a  differ- 
ent scale  —  in  the  expectation  that  the  result  will  be  the  same. 
Every  departure  must  be  compensated  by  some  other  —  a  change 
in  material  by  a  change  in  the  size  or  distribution  of  the  audience, 
or  perhaps  by  a  partly  compensating  change  in  the  material  used 
in  some  other  part  of  the  hall  —  a  change  in  size  by  a  change  in 
the  proportions  or  shape.  For  moderate  departures  from  the 
model  such  compensation  can  be  made,  and  the  model  will  serve 
well  as  a  guide  to  a  first  approximation.  When  the  departure  is 
great  the  approved  auditorium,  unless  discriminatingly  used,  is 
liable  to  be  a  treacherous  guide.  In  tin's  case  the  departure  was 
necessarily  great. 

The  comparison  of  halls  should  be  based  on  the  duration  of  the 
residual  sound  after  the  cessation  of  a  source  that  has  produced 
over  the  hall  some  standard  average  intensity  of  sound,  —  say  one 
million  times  the  minimum  audible  intensity,  1,000,000  i'.  The 
means  for  this  calculation  was  furnished  in  the  fifth  paper.  The 
values  of  T'  and  a  for  the  three  halls  under  comparison  are  shown 
on  the  next  page. 

Tlu>  length  given  for  the  Leipzig  Gewandhaus,  88  meters,  is 
measured  from  the  organ  front  to  the  architecturally  principal  wall 
in  the  rear.  On  the  floor  and  by  boxes  in  the  balconies  the  seats 
extend  3  meters  farther  back,  making  the  whole  length  of  the  hall, 
exclusive  of  the  organ  niche,  41  meters.  This  increases  the  vohune 
of  the  hall  about  '200  cubic  meters,  making  the  total  volume  11,400 
cubic  meters. 

'IIic  lieight  givi'U  for  the  new  Boston  Music  Hall,  17.!),  is  the 
average  heiglit  from  the  sloping  floor.  The  length  is  measured  on 
the  floor  of  the  main  part  of  the  hall;  aboxc  the  second  gallery  it 
extends  back  !-2.74  meters,  giving  an  adilitional  volume  of  380  cubic 
meters.  The  stjige,  instead  of  being  out  in  the  room,  is  in  a  con- 
tracted recess  having  a  depth  of  7.!)  meters,  a  breadth,  front  and 
back,  of  18.8  ami  1.8.0.  respectively,  and  a  height,  front  and  back, 
of  13.4  and  10.0,  resjiectively,  with  a  volume  of  l,oOO  cubic  meters. 
The  height  of  the  stage  recess  is  determined  by  the  absolute  re- 


(il 


RKNKRRKRATIOX 
Dimensions  of  the  Three  Hali;s  in  Meters  ' 


I^nfrth . 
Hmiilth 
tlfight 

Volume . 


LeJDiiK  Gcvaodhaiu     Boston  Music  Hall.      Boston  Music  Hall, 
Old  New 


(luiroiiu'iits  ol'  (lif  lar^H'  orKaii  lu  be  buill  l)y  Mr.  George  S.  Hutch- 
ings.  This  organ  will  extend  across  the  whole  breadth  of  the  stage. 
The  lohil  volume  of  thf  new  Roston  Music  Hall  is,  therefore, 
1S..'50U  cubic  meters. 

In  the  following  table  of  materials  in  the  three  halls  no  distinction 
is  made  between  plaster  on  wire  lath  and  plaster  on  wood  lath,  the 
experiments  recorded  in  tlie  preceding  paper  having  shown  no  cer- 
tain difference  in  absorbing  power.  The  areas  of  wall-surface  are 
exi)ressi'd  in  s(|uare  meters.  The  number  of  persons  in  the  audience 
is  reckoned  from  the  number  of  seats,  no  account  being  taken  of 
standing  room. 

'  Dlmensions  of  the  Thuke  Halls  ix  Feet 


Leipzig 
Ge wand ha us 


Boston  1  Boston 

Music  Hall.  Old        Music  Hall.  New 


Letigth. 
Breadth 
Height . 

Volume. 


(130) 
75 
59 

(575,000) 


The  length  given  for  the  I>eipzig  Gcwandhaus,  144  feet,  is  measured  from  the  organ  front 
to  the  arohite<-luralIy  principal  wall  in  the  rear.  On  the  floor  and  by  boxes  in  the  balconies 
the  seats  extend  10  feet  farther  back,  making  the  total  length  of  the  hall,  exclusive  of  the 
organ  niche.  1S4  feet.  This  increases  the  volume  7,000  cubic  feel,  making  the  total  volume 
■t(l7,(MH)  cul)ic  feet. 

The  height  given  for  the  new  liiill,  .")!)  feel,  is  the  average  height  from  the  sloping  floor. 
The  length  is  measured  on  the  HiMir  of  the  main  part  of  the  hall;  above  the  second  gallery  it 
extends  back  !)  feet,  giving  an  adilitional  volume  of  '20,000  cubic  feet.  The  stage,  instead  of 
being  out  in  the  room,  is  in  a  contracted  recess,  having  a  depth  of  "iii  feet,  a  breadtii,  front  and 
buck,  of  fit)  feet  and  45  feet,  respectively,  and  a  height,  front  and  back,  of  44  feet  and  35  feet, 
respectively,  with  a  volume  of  54,000  cubic  feet.  The  total  volume  of  the  new  Music  Hall  is, 
therefore,  r)4n,0(tn  i  ubic  feet. 


CALCULATION  IN  CONSTRUCTION 


65 


Absorbing  Material 


Leipzig 
Gewandhaus 


Boston  Music  Hall, 
Old 


Boston  Music  Hall, 
New 


Piaster  on  lath  . 
I'histtT  on  tilo.  . 

(;lass 

Wood 

Drapery 

Audience: 

on  floor 

in  Isl  l>aleony 
in  2d  balcony 

Total  audience. 

Orchestra 


2,200 

0 

17 

233 

80 

990 

494 

33 

1,.-.17 

80 


3,030 

0 

55 

771 

4 

1,251 
C80 
460 

2,391 

80 


1,040 

1,830 

22 

C25 

0 

1,400 
(iOO 
507 

2,579 

80 


'I'lic  (Inipcry  in  I  In-  Leipzig  Gewandhaus  will  he  rated  as  shelia, 
and  in  I  lie  old  Music  Hall  as  cretonne,  to  which  it  approximates  in 
each  case.  It  is  an  almost  needless  nfiiuincnl  to  rate  differently 
the  orchestra  and  the  audience  merely  because  the  members  of  the 
orchestra  sit  more  or  less  clear  of  each  other,  but  for  the  sake  of  a 
certain  formal  completeness  it  will  be  done.  For  the  above  materials 
the  coefficients,  taken  from  the  preceding  paper,  are  as  follows: 

Coefficients  of  Absorption 

Plaster  on  latii 033 

Plaster  on  tile 025 

Class 027 

Wood 061 

/  shelia 23 

Drapery   <        ,  ,- 

[  cretonne »•> 

Audience  per  person 44 

Orchestra  per  man 48 

In  Ihe  table  (p.  07)  is  entered  liie  total  absorbing  power  con- 
tributed by  each  of  these  elements.  As  this  is  the  first  example  of 
such  cilciil;!!  loll  ;ill  ihc  clcmciils  will  be  slinwn.  a!llioui;li  it  will 
liiiii  be  iimiiediateiy  evidnit  that  noimc  are  of  wholly  negligible 
magnil  udc. 


—.7  8    »l.- 


FiG.  20.     The  Leipzig  Gewandhaus. 


.-Lmut 


ijuyimji 


n     B  III — t 


H 


a 


Q. 


ffl  IfflllfflllB 


M 


301 


■:iu.-i  ni.- 


I-IG.  il.     The  Old  Boston  Music  Hall. 


3».5  m- 


FiG.  ii.     The  New  Boston  Music  Hall. 


CALCULATION  IN  CONSTRUCTION 


67 


Absorbing  Power 


Leipzig 
Gewandhaus 

Bostoa  Music  Hall, 
Old 

Boston  Music  Hall, 
New 

Plaster  on 

lath 

73 

II 

0.4 

14 

18 

667 

38 

100 
0 

1.5 
47 
0.6 
1,052 
38 

34 

Piaster  on 

tile 

46 

Glass 

0.6 

Wood 

38 

Drapery 

0 

Audience 

1,135 

Orchestra 

38 

Total  =  a 

810 

1,239 

1,292 

V  and  a  being  determined  for  each  of  the  three  halls,  the  dura- 
tion, T,  of  the  residual  sound  after  standard  initial  intensity  can  be 
calculated. 

The  results,  in  seconds,  are  as  follows: 

Leipzig  Gewandhaus 'i.SO 

Old  Boston  Music  Hall ^.44 

New  Boston  Music  Hall '2.31 

In  other  words,  the  new  hall,  although  having  a  seating  capacity 
for  over  a  thousand  more  than  the  Gewandhaus  and  nearly  two 
hundred  more  than  the  old  hall,  will  have  a  reverberation  between 
the  two,  and  nearer  that  of  the  Gewandhaus  than  that  of  the  old 
hall. 

It  is  interesting  to  contra.st  this  with  the  result  that  would  have 
been  obtained  had  the  plan  been  followed  of  reproducing  on  an  en- 
larged scale  the  Gewandhaus.  Assuming  perfect  reproduction  of 
all  proportions  with  like  materials,  the  volume  would  have  been 
25,300  cubic  meters,  and  the  absorbing  power  1,370,  resulting  in  the 
value,  T  =  3.0'2.  This  woulil  have  differed  from  the  chosen  result 
l)y  an  amount  tiiat  would  have  l)een  very  noticeable. 

The  new  IJoston  Music  Hall  is,  therefore,  not  a  copy  of  tiie 
Gewandhaus,  but  tlie  desired  results  have  been  attained  in  a  very 
different  way. 

A  few  general  considerations,  not  directly  c(mnected  with  rever- 
beration, UKiy  be  of  interest.  The  three  halls  are  of  nearly  the  same 
length  on  the  floor;   but  in  the  old  hall  and  in  the  Gewandhaus  the 


68  Hi:M;i{i{i;RAri()X 

plat  form  for  tin*  orclu-stra  is  out  in  I  lie  liall.  and  tlu'  f,'aIl(Tie.s  extend 
alon^r  l)olli  sides  of  it;  wliile  in  the  new  hull  Ihe  orchestra  is  not  out 
in  tile  main  hody  of  tlie  room,  and  for  this  roivson  is  slightly  farther 
from  the  rear  of  the  hall;  l)ut  this  is  more  than  compensated  for  in 
respec'l  to  loudness  by  the  orchestra  being  in  a  somewhat  contracted 
stage  recess,  from  the  side  walls  of  which  the  reflection  is  better 
l)eeause  they  are  nearer  and  not  occupied  by  an  audience.  Also  it 
may  be  noted  that  the  new  hall  is  not  so  high  as  the  old  and  is  not 
so  broad. 

Thus  is  opened  up  the  ([uestion  of  loudness,  and  this  has  been 
solved  to  a  first  ajiproximation  for  the  case  of  sustained  tones. 
But  as  the  series  of  papers  now  conchided  is  devoted  to  the  question 
of  reverberation,  this  new  problem  must  be  reserved  for  a  subse- 
quent discussion. 


ARCHITFXTURAL   ACOUSTICS^ 

INTRODUCTION 

1  HE  prohk'in  of  iircliiti'ctiiral  ucoiislics  ri'ciuiivs  for  its  complete 
solution  two  distinct  lines  of  invest ij^at ion,  one  to  determine  (|iian- 
titatively  the  physical  conditions  on  which  loudness,  reverberation, 
resonance,  and  the  allied  phenomena  depend.  I  lie  oilier  to  deleriiiine 
the  intensity  which  each  of  these  should  have,  what  conditions  are 
best  for  the  distinct  audition  of  sjjeech.  and  what  effects  are  best  for 
music  in  its  various  forms.  One  is  a  purely  ])hysical  investigation, 
and  ils  conclusions  should  be  based  an<l  ^lll>uld  be  disputed  only  on 
scientific  grounds;  the  other  is  a  matter  of  judf^iiient  and  taste,  and 
its  conclusions  are  weif.rhly  in  ])ro|)orl  ion  to  the  weight  and  unaiiinutj' 
of  the  iiuthorily  in  which  they  find  their  source.  For  this  re;uson, 
these  pajHTs  are  in  two  series,  'ihe  articles  which  appeared  six 
years  ago  began  the  first,  and  the  |)a])er  immediately  following  is 
the  begimu'ng  of  the  second. 

Of  the  first  .series  of  papers,  which  have  to  do  with  the  ])urely 
physical  side  of  the  problem,  only  one  pajjcr  has  as  yet  been  i)ub- 
lislicd.  'I'his  conlaiiied  a  di.scussion  of  reverberation,  eomplele  as 
far  as  one  note  is  concerned.  There  is  on  hand  considerable  material 
for  a  paper  I'xiending  this  discussion  to  cover  the  whole  range  of  the 
musical  scale,  and  therefore  furiii>liing  a  basis  for  the  discussion  of 
whiit  has  sometimes  been  called  the  musical  (|iiality  of  an  audito- 
rium, 'i'lii'i'e  li.i-  also  l>eeu  eolieeled  a  eerlaiu  amount  of  data  ill 
regard  to  loudni-ss.  resonance,  interference,  eclux's,  irregularitit's  of 
air  curri'nts  and  lemperalure,  and  the  transmission  of  sound  through 
walls  and  partiti(jns,  —  all  of  which  will  ajipear  as  soon  as  a  com- 
plete ]n-esentation  is  j)ossil)le  in  each  (  a>e.  i'l.ieh  pri(l)lem  iia^  lieen 
taken  up  as  it  has  been  brought  to  the  writer's  attention  by  an 
architect  in  coiisullal ion  either  o\-er  |)lans  or  in  regard  to  a  coin- 
ph'ted  buihling.      lliis  method  is  slow,  but  it  has  Ihe  advantage  of 

'  l'r<)Of<iling.s  (if  tile  .Viiicriran  .\(iulomy  nf  .\rls  iiiul  .Scit-iK-cs,  vol.  xlii,  no.  i, .Iiiiio,  lOIIO. 

(Ill 


70  AH(  IIITECn'RAL  ACOUSTICS 

riiakiiig  (Ik-  work  i)r;iclic;il.  and  may  Ix-  rt-lii'd  on  lo  i)rev(.'iil  the 
inafinificalion  to  undue  importance  of  scientifically  interesting  but 
practically  subordinate  points.  On  the  other  hand,  there  is  the 
danger  liiat  it  may  lead  to  a  fragmentary  jjresciilation.  An  effort 
has  been  made  to  guard  against  this,  and  the  effort  for  completeness 
is  the  reason  for  delay  in  the  appearance  of  some  of  the  papers. 
Sufficient  jjrogress  has  been  made,  however,  to  justify  the  assertion 
llial  the  physical  side  of  the  problem  is  solvable,  and  that  it  should 
be  possible  ultimately  to  calculate  in  advance  of  construction  all 
the  acoustical  (|ualilies  of  an  auditorium. 

'riiu>  far  it  is  a  legitimate  problem  in  physics,  and  as  such  a 
reasonable  one  for  the  writer  to  undertake. 

The  second  part  of  the  problem,  now  being  started,  the  question 
as  to  what  constitutes  good  and  what  constitutes  poor  acoustics, 
what  effects  are  desirable  in  an  auditorium  designed  for  speaking, 
and  even  more  especially  in  one  designed  for  music,  is  not  a  question 
in  physics.  It  is  therefore  not  one  for  which  the  writer  is  especially 
qualified,  and  would  not  be  undertaken  here  were  it  not  in  the  first 
place  absolutely  necessary  in  order  to  give  effect  to  the  rest  of  the 
work,  and  in  the  second  place  were  it  not  the  plan  rather  to  gather 
and  give  expression  to  the  judgment  of  others  acknowledged  as 
(|ualified  to  speak,  than  to  give  expression  to  the  taste  and  judg- 
ment of  one.  It  is  thus  the  purpose  to  seek  expert  judgment  in 
regard  to  acoustical  effects,  and  if  possible  to  present  the  results  in 
a  form  available  to  architects.  This  will  be  slow  and  difficult  work, 
and  it  is  not  at  all  certain  that  it  will  be  possible  to  arrive,  even  ulti- 
mately, at  a  finished  product.  It  is  worth  undertaking,  however,  if 
the  job  as  a  whole  is  worth  undertaking,  for  without  it  the  physical 
side  of  the  investigation  will  lose  much  of  its  practical  value.  Thus 
it  is  of  little  value  to  be  able  to  calculate  in  advance  of  construction 
and  express  in  numerical  measure  the  acoustical  quality  which  any 
planned  auditorium  will  have,  unless  one  knows  also  in  numerical 
measure  the  acoustical  quality  which  is  desired.  On  the  other  hand, 
if  the  owner  and  the  architect  can  agree  on  the  desired  result,  and 
if  this  is  within  the  limits  of  possibility  considering  all  the  demands 
on  the  auditorium,  of  utility,  architecture,  and  engineering,  this 
result  can  be  secured  with  certainty,  —  at  least  there  need  be  no 


ACCrRACY  OF  MUSICAL  TASTE  71 

uncertainty  as  to  wlu-tlu'r  it  will  or  will  not  be  attained  in  the  com- 
pleted building. 

The  papers  following  this  introduction  will  be:  The  Accuracy  of 

Musical  Taaie  in  regard  to  A rr/iifertiiral  Acoustics,  and  Variation  in 
Reverberation  with   J'ariation  in  Pitch. 


riri-;  accuracy  of  musical  taste  ix  regard 
TO  architectural  acoustics 

PIANO    MUSIC 

1  HE  experiments  described  in  this  paper  were  undertaken  in  order 
to  determine  the  reverberation  best  suited  to  piano  music  in  a  music 
room  of  moderate  size,  but  were  so  conducted  as  to  give  a  measure  of 
the  acc-uracy  of  cultixaLcd  lunsical  iasle.  Tlie  lattiT  jjoint  is  ()l)vi- 
ously  fundamental  to  the  whole  investigation,  for  unless  musical 
taste  is  precise,  the  ])r()b!em.  at  least  as  far  as  it  concerns  the  design 
of  the  auditorium  for  nuisical  purposes,  is  indeterminate. 

The  first  ()l)S('r\atii)ns  in  regard  to  the  precision  of  nuisical  taste 
were  obtained  during  tlic  plaiming  of  the  Boston  Sjmiphony  Hall, 
Messrs.  McKim,  Mead,  and  White,  Architects.  Mr.  Higginson, 
Mr.  Gericke.  the  conduc-tor  of  tlie  orchestra,  and  others  connected 
with  the  Building  Conunittee  expre.s.sed  opinions  in  regard  to  a 
number  of  auditoriums.  These  buildings  included  the  old  Boston 
Music  Hall,  at  that  time  the  home  of  the  orchestra,  and  the  places 
visited  l)v  the  orchestra  in  its  winter  trips,  Sanders  Theatre  in 
Cambridge,  Carnegie  Hall  in  New  York,  the  Academy  of  Music  in 
Philadelphia,  and  the  Music  Hall  in  Baltimore,  and  in  addition  to 
these  the  Leipzig  Gewandliaus.  By  invitation  of  Mr.  Higginson, 
the  writer  accompanied  the  orchestra  on  one  of  its  tri])s,  made 
measurements  of  all  the  hails,  and  calculated  their  reverberation. 
The  dimensions   ami    I  lie    in.ilcri.d    of   I  lie  Gewandhaus    had    been 

publislied,  and  IV Ihesedala  its  re\-ci-l)craliiin  also  was  cah-ulated. 

The  results  of  lhe.se  mciusm-ements  and  calculations  showeil  that  the 
opinions  expressed  in  regard  to  the  several  halls  were  entirely  con- 
sistent with  the  physical  facts.  That  is  to  say,  the  reverberation  in 
those  halls  in  wiiidi  il  was  declared  too  gn-at  was  in  point  of  physi- 
cal meiisuremenl   greater  than  in  halls  in  which  it   was  i)ronouncetl 


7^2  Ai{(  iirrK(Tn{Ai>  acoistks 

loo  small.  This  coiisisU-iicy  gavf  i-ncoiirafrciiUMit  in  tlic  liope  tliat 
fill'  pliysical  proMi-iu  was  rral,  ami  tin-  ciul  to  lu'  allaiiied  definite. 

Mucli  more  <-lal)(>rate  data  on  the  accuraey  of  musical  taste  were 
ol)tainfii  four  yt'ar>  lalcr.  l!t(»-',  in  coniiccl  ion  with  the  new  l)uililiii<,' 
of  the  New  England  Conservatory  of  Miisie,  Messrs.  Wheelwright 
and  Haven.  Architects.  The  new  building  consists  of  a  large  audi- 
torium surrounded  on  three  sides  hy  smaller  rooms,  which  on  the 
.second  and  lliird  floors  are  used  for  purposes  of  instruction.  These 
smaller  rooms,  wlicn  first  occupied,  and  used  in  an  unfurnished  or 
j)artially  furnished  condition,  were  found  unsuital)le  acoustically, 
and  the  writer  wius  consulted  by  Mr.  Haven  in  regard  to  their  final 
adjustment.  In  order  to  learn  the  acoustical  condition  which  would 
accural cly  nucl  the  requirements  of  those  who  were  to  use  the 
rooms,  an  experiment  was  undertaken  in  which  a  number  of  rooms, 
chosen  as  tyi)ical.  were  varied  rapidly  in  resjject  to  reverberation  by 
means  of  temporarily  introduced  absorbing  material.  Approval  or 
disai)])roval  of  I  lie  acoustical  quality  of  each  room  at  each  stage  was 
expressed  by  a  connnittee  chosen  by  the  Director  of  the  Conserva- 
tory. At  the  close  of  these  tests,  the  reverberation  in  the  rooms  was 
mciisured  by  the  writer  in  an  entirely  indci)cndcut  nuinner  as 
described  in  the  paper  on  Reverberation  (1900).  The  judges  were 
Mr.  (leorge  W.  Chadwick,  Director  of  the  Conservatory,  and  Signor 
Orcsti  Binibom',  Mr.  William  H.  Dunham,  Mr.  George  W.  Proctor, 
anil  Mr.  William  L.  Whitney,  of  the  Faculty.  The  writer  suggested 
and  arranged  the  experiment  and  subsequently  reduced  the  results 
!o  muncrical  measure,  but  expressed  no  opinion  in  regard  to  the 
quality  of  the  rooms. 

The  merits  of  each  room  in  its  varied  conditions  were  judged 
solely  by  listening  to  piano  music  by  ]Mr.  Proctor.  The  character 
of  the  nui>i(al  compositions  on  which  the  judgment  was  based  is  a 
matter  of  interest  in  this  connection,  but  this  fact  was  not  appre- 
ciated at,  the  time  and  no  record  of  the  selections  was  made.  It  is 
only  |)ossible  to  say  that  several  short  fragments,  varied  in  nature, 
were  tried  in  eacli  room. 

As  will  be  evident  from  the  descriptions  given  below,  the  rooms 
were  so  differently  furnished  that  no  inference  as  to  the  reverbera- 
tion could  be  drawn  from  appearances,  and  it  is  certain  tliat  the 


ACClTiACY  OF  :\IT;SirAL  TASTE  73 

opinions  were  htused  .solely  on  I  lie  qii;ilil\'  ol'  Uie  room  as  heard  in 
the  i)iiino  music. 

The  five  rooms  chosen  as  typical  were  on  the  second  floor  of  I  lie 
buildinf:^.  The  rooms  were  four  meters  high.  Their  volumes  varied 
from  74  to  '210  cubic  meters.  The  walls  and  ceilinjjs  were  finished  in 
plaster  on  wire  lath,  and  were  neither  papered  nor  painted.  There 
was  a  piano  in  each  room;  in  room  .5  there  were  two.  Tiie  amount 
of  other  iiirniture  in  tlie  rooms  varied  <,n'eatly: 

In  room  1  there  was  a  hare  floor,  and  no  furniture  excej)t  the 
piano  and  piano  stool. 

Room  '■2  had  rugs  on  the  floor,  chairs,  a  sofa  with  pillows,  table, 
music  racks,  and  a  lanij). 

Room  :>  had  a  carpet,  chairs,  bookcases,  and  a  large  number  of 
books,  which,  overflowint;  I  lie  bookcases,  were  stacked  along  the 
walls. 

Room  4  had  no  carpet,  but  there  were  chairs  and  a  small  table. 

Room  5  had  a  carpet,  chairs,  and  shelia  curtains. 

Thus  the  rooms  varied  from  an  almost  unfurnished  to  a  reasonaI)ly 
furnished  condition.     In  all  eases  the  reverberation  was  too  great. 

The  experiment  was  begun  in  room  1.  Tliere  were,  at  the  time, 
besides  the  writer,  five  gentlemen  in  the  room,  the  absorbing  effect 
of  whose  clothing,  though  small,  nevertheless  should  be  taken  into 
account  in  an  accurate  calculation  of  the  reverberation.  Thirteen 
cushions  from  the  seats  in  Sand<'rs  Theatre,  whose  absorl)ing  power 
for  sound  liad  been  deterinined  in  an  earliei'  investigation,  were 
brought  into  the  room.  I'nder  tliese  conditioTi>  the  imanimous 
opinion  was  that  the  room,  as  tested  by  the  piano,  was  lifeless.  'I'wo 
cushions  were  then  removed  from  the  room  with  a  perceptible  change 
for  the  beltei-  in  the  piano  nuisic.  'i'hree  more  cushions  were  re- 
moved, and  tlieetfect  was  iimkIi  lutler.  'l\vo  more  were  then  taken 
out,  leaving  six  cushions  in  I  lie  room,  and  I  lie  re>iilt  met  unanimous 
approval.  It  was  suggested  liiat  two  more  be  removetl.  This  l)eing 
done  the  re\-erberal  ion  was  found  to  be  loo  great.  The  agreement 
was  then  reached  tlial  the  conditions  produced  by  tlu-  presi-nce  ol 
si.\  cushions  were  the  most  nearly  satisfactory. 

The  e\|)erinu'nt  was  tiu'U  contimied  in  Mr.  Dunham's  ro(»m, 
numl)er   ^i.      Six   gentlemen    were   present.      Seven    cushions    were 


74  AHCmrKCTrUAL  ACOUSTICS 

hroiijjlit  into  tlio  room.  'I'lif  music  showed  an  insiifficiont  rever- 
iHTiilion.  Two  of  the  cusliions  wt-ro  tlien  taken  out.  The  change 
was  reganled  as  a  distinct  improvement,  and  the  room  was  satis- 
factory. 

Tn  yir.  Wliitney's  room,  number  3,  twelve  cushions,  with  which 
it  w;us  th(>uf,'ht  to  overload  the  room,  were  found  insufficient  even 
with  the  presence  in  this  case  of  seven  gentlemen.  Three  more 
cushions  were  brought  in  and  the  result  declared  satisfactory. 

In  llif  fourth  room,  five,  eight,  and  ten  cushions  were  tried  be- 
fore the  conditions  were  regarded  as  satisfactory. 

In  Mr.  Proctor's  room,  number  5,  it  was  evident  that  the  ten 
cushions  which  had  been  brought  into  the  room  had  overloaded  it. 
Two  were  removed,  and  afterwards  three  more,  leaving  only  five, 
before  a  satisfactory  condition  was  reached. 

This  completed  the  direct  experiment  with  the  piano. 
The  i)ringing  into  a  room  of  any  absorbing  material,  such  as  these 
cushions,  affects  its  acoustical  properties  in  several  respects,  but 
principally  in  respect  to  its  reverberation.  The  prolongation  of 
sound  in  a  room  after  the  cessation  of  its  source  may  be  regarded 
either  ;ls  a  case  of  stored  energy  which  is  gradually  suffering  loss  by 
transmission  through  and  absorption  by  the  walls  and  contained 
material,  or  it  may  be  regarded  as  a  process  of  rapid  reflection  from 
wall  to  wall  with  loss  at  each  reflection.  In  either  case  it  is  called 
reverberation.  It  is  sometimes  called,  mistakenly  as  has  been  ex- 
jilained,  resonance.  The  reverberation  may  be  expressed  by  the 
duration  of  audibility  of  the  residual  sound  after  tjie  cessation  of  a 
source  so  adjusted  as  to  produce  an  average  of  sound  of  some  stand- 
ard intensity  over  the  whole  room.  The  direct  determination  of 
this,  under  the  varied  conditions  of  this  experiment,  was  impracti- 
cable, but,  by  measuring  the  duration  of  audibility  of  the  residual 
sound  after  the  cessation  of  a  measured  organ  pijx'  in  each  room 
without  any  cushions,  and  knowing  the  coefficient  of  absorption  of 
the  cushions,  it  was  jiossible  to  calculate  accurately  the  reverbera- 
tion at  each  stage  in  the  test.  It  was  impossible  to  make  these 
measurements  inunediately  after  the  above  experiments,  because, 
although  the  day  wjis  an  especially  quiet  one,  the  noises  from  the 
street  and  railway  traffic  were  seriously  disturbing.    Late  the  follow- 


ACCURACY  OF  MUSICAL  TASTE 


to 


iiig  night  the  conditions  were  more  favorable,  and  a  series  of  fairly 
good  observations  was  obtained  in  each  room.  ITie  cushions  had 
been  removed,  so  that  the  measurements  were  made  on  the  rooms  in 
their  original  condition,  furnished  as  above  described.  The  appara- 
tus and  method  employed  are  described  in  full  in  a  series  of  articles 
in  the  Engineering  Record  '  and  American  Architect  for  1900. 
The  results  are  given  in  the  accompanying  table. 


J 
i 

z 

I 

<£ 

Gentlemen  Present 

9 

u  = 

.e:s 

■£c 

NiiiiilxT  of  Meters 
of  Cushions 

Absorbing  Power 
of  Cushions 

Total  Absorbing 
Power 

Reverberation  in 
Seconds 

Remarks 

1 

74 

5.0 

0 

0 

0 

0 

5.0 

2.43 

Reverberation  too  great. 

U 

5 

2.4 

(1 

0 

7.4 

1.64 

Reverberation  too  great. 

a 

u 

u 

13 

12.8 

20.2 

.60 

Reverberation  too  little. 

a 

u 

U 

11 

10.1 

17.5 

.70 

Better. 

M 

a 

u 

8 

7.3 

14.7 

.83 

Better. 

U 

u 

u 

(i 

5.5 

12.9 

.95 

Condition  approved. 

a 

u 

u 

4 

3.(i 

11.0 

1.22 

Reverberation  too  great. 

i 

91 

6.3 

0 

0 

0 

0 

(I.;! 

2.39 

Reverberation  too  great. 

u 

6 

2.9 

0 

(1 

9.2 

1.95 

Reverberation  too  great. 

a 

U 

'• 

7 

(i.4 

15.(i 

.95 

Reverberation  too  little. 

u 

u 

u 

.5 

4.G 

l;!.8 

1.10 

Condition  approved. 

S 

210 

14.0 

0 

0 

0 

0 

14.0 

2.40 

Reverberation  too  great. 

U 

7 

3.4 

0 

0 

17.4 

2.00 

Reverberation  too  great. 

u 

tt 

tt 

12 

11.0 

28.4 

1.21 

Better. 

a 

tt 

u 

15 

13.7 

31.1 

1.10 

Condition  approved. 

4 

133 

8.8 

0 

0 

0 

0 

8.3 

2.65 

Reverberation  too  great. 

U 

7 

3.4 

0 

0 

11.7 

1.87 

Reverberation  too  great. 

u 

a 

u 

6 

5.5 

17.2 

1.2(i 

Better. 

u 

u 

u 

10 

9.1 

20.8 

1.09 

Condition  approved. 

5 

96 

7.0 

0 

(1 

(1 

0 

7.0 

2.24 

Reverberation  too  great. 

'  « 

4 

l.i) 

0 

0 

8.9 

1.76 

Reverberation  too  great. 

tt 

u 

U 

10 

9.1 

18.0 

.87 

Reverberation  too  little. 

u 

u 

u 

8 

7.3 

16.2 

.98 

Belter. 

u 

u 

u 

5 

4.6 

13.5 

1.16 

Condition  approved. 

<  The  iirticle  in  tlie  Engineering  Record  is  identical  willi   llio  paper  in  llie  .Xmoritun 
Architect  for  1900,  reprinted  in  thi.s  volume  a»  I'arl  1. 


76  Al{(  IHTKCnUAI.  ACOUSTICS 

The  lahlo  is  a  n-coril  of  tin-  first  of  \vli;it.  it  is  liopcd,  will  he  a 
series  of  siieli  exi)eriinents  extending'  to  rooms  of  iiukIi  larger  dinien- 
sioiis  and  to  oilier  kinds  of  inusie.  It  may  well  he,  in  fact  it  is 
hiphly  ])rohahle.  tliat  very  much  larger  rooms  would  necessitate  a 
dilfcnnl  amount  of  reverheration,  lus  also  may  other  types  of  musical 
instruments  or  the  voice.  As  an  example  of  such  investigations,  as 
well  as  evidence  of  their  need,  it  is  here  given  in  full.  The  foHowing 
additional  explanations  may  be  made.  The  variation  in  volume  of 
the  rooms  is  only  threefold,  corresponding  only  to  such  music  rooms 
as  may  he  found  in  private  houses.  Over  this  range  a  j)erceptihle 
variation  in  the  retpiired  reverheration  should  not  he  expected.  The 
third  colunm  in  the  table  inchules  in  the  absorbing  power  of  the 
room  (ceiling,  walls,  furniture,  etc.)  the  absorbing  powers  of  the' 
clothes  of  the  writer,  who  was  present  not  merely  at  all  tests,  but  in 
the  measurement  of  the  reverberation  the  following  night.  From 
the  next  two  columns,  therefore,  the  writer  and  the  effects  of  his 
clothing  are  omitted.  The  remarks  in  the  last  column  are  reduced 
to  the  form  "reverberation  too  great,"  "too  little,"  or  "ajiproved." 
The  remarks  at  the  time  were  not  in  this  form,  however.  The  room 
was  ])ronoimced  "too  resonant,"  "too  much  echo,"  "harsh,"  or 
"dull,"  "lifeless,"  "overloaded,"  expressions  to  which  the  forms 
adopted  are  equivalent. 

If  from  the  larger  table  the  reverberation  in  each  room,  in  its 
most  approved  condition,  is  separately  tabulated,  the  following  is 
obtained : 

Roonu  Reverberation 

1 95 

2 1.10  ^ 

3 1.10 

4 l.Oi) 

5 1.16 

1.08  mean 

The  final  result  obtained,  that  the  reverberation  in  a  music  room 
in  order  to  secure  the  best  effect  with  a  piano  should  be  1.08,  or  in 
round  numbers  1.1,  is  in  itself  of  considerable  practical  value;  but 
the  five  determinations,  by  their  mutual  agreement,  give  a  numeri- 
cal meiusure  to  the  accuracy  of  musical  taste  which  is  of  great 
interest.  Thus  the  maximum  departure  from  the  mean  is  .13  seconds, 


ACCURACY  OF  MTTSICAL  TASTE  77 

and  the  avi-ragc  (IciKirlure  is  .05  seconds.  Five  is  ratlier  a  snudl 
number  of  observations  on  which  to  apply  the  theory  of  probaliilities, 
bill,  assuming  that  it  justifies  such  reasoning,  the  probable  error  is 
.O"^  seconds,  —  surprisingly  small. 

A  clo.se  in.spection  of  the  large  lal)le  will  bring  out  an  interesting 
fact.  The  room  in  which  the  approved  condition  differed  most  from 
the  mean  was  the  first.  In  this  room,  and  in  this  room  only,  was  il 
suggested  by  the  gentlemen  present  that  the  experiment  should  be 
carried  further.  This  was  done  by  removing  two  more  cushions. 
The  reverberation  was  then  l.'-H  seconds,  and  this  was  decided  to 
be  too  much.  'I'he  ])oiut  to  be  observed  is  that  l.'2^2  is  further  above 
tlic  nuiiii,  l.OS,  tliaii  .95  is  below.  Moreover,  if  one  looks  over  the 
list  in  each  room  it  will  be  seen  that  in  every  case  the  reverberation 
corresponding  to  the  chosen  condition  came  nearer  to  the  mean  than 
that  of  any  other  condition  tried. 

It  is  conceivable  tlial  had  the  rooms  been  alike  in  all  respects  and 
required  the  same  amount  of  cushions  to  accomplish  the  same  re- 
sults, the  experiment  in  one  room  might  have  j)rejudiced  the  ex- 
periment in  tlu'  next.  But  tlie  rooms  being  diiVerent  in  size  and 
furnished  so  differently,  an  impression  formed  in  one  room  as  to  the 
iininlicr  of  cushions  necessary  could  only  be  misleading  if  depended 
on  in  the  next.  Thus  the  several  rooms  re(|uired  (>,  5,  15,  10,  and  5 
cushions.  It  is  further  to  be  ob.served  that  in  three  of  the  rooms  the 
final  condition  was  reached  in  working  from  an  overloaded  con- 
dition, and  in  llic  oilier  two  rooms  from  the  opposite  condition, — 
in  the  one  case  by  taking  cushions  out.  and  in  the  other  by  bringing 
them  in. 

Before  bcgiiiiiiiig  I  lie  exi)eriiiieiit  no  explaiial  ion  was  made  of  its 
nature,  and  no  di.scussion  was  held  as  to  the  adxantages  and  disad- 
vantages of  re\('il)(ialion.  '{"lie  gentlemen  present  were  asked  to 
express  their  a|)])roval  or  disapproval  of  the  room  at  each  stagt'  of 
the  experiment,  and  the  iiiial  ilecision  seemed  to  be  reached  with 
perfectly  free  unanimil.w 

This  surprising  accuracy  of  nuisical  taste  is  perhaps  the  explana- 
tion of  the  rarity  with  which  it  is  entirely  satisfied,  particularly 
when  the  arciiilectiiral  designs  are  left  to  chance  in  this  res])ecl. 


78  Al{<  IHTi;(   irHAL  ACOUSTICS 

\AIUATI()N   IN   REVKRBERATIOX   WITH 
\  AIUAI'IOX  IX  PITCH 

Six  yoars  ago  thero  wjus  published  in  the  Engineering  Record  and 
the  American  Architect  a  series  of  papers  on  architectural  acoustics 
intended  as  a  heginning  in  the  general  subject.  The  particular  phase 
of  the  subject  under  consideration  was  reverberation,  —  the  continua- 
tion of  sound  in  a  room  after  the  source  has  ceased.  It  was  there 
shown  to  depend  on  two  things, — the  volume  of  the  room,  and  the 
absorbing  character  of  the  walls  and  of  the  material  with  which  the 
room  is  filled.  It  was  also  mentioned  that  the  reverberation  depends 
in  special  cases  on  the  shape  of  the  room,  but  these  special  cases  were 
not  considered.  Tlie  present  paper  also  will  not  take  up  these  special 
cases,  but  postpone  their  consideration,  although  a  good  deal  of 
material  along  this  line  has  now  been  collected.  It  is  the  object 
here  to  continue  the  earlier  work  rather  narrowly  along  the  original 
lines.  The  subject  was  then  investigated  solely  with  reference  to 
sounds  of  one  pitch,  C4  512  vibrations  per  second.  It  is  the  inten- 
tion here  to  extend  this  over  nearly  tlic  wliole  range  of  the  musical 
scale,  from  Ci  G4  to  ('7  4096. 

It  can  be  shown  readily  that  the  various  materials  of  which  the 
walls  of  a  room  are  Constructed  and  the  materials  with  which  it  is 
filled  do  not  have  the  same  absorbing  power  for  all  sounds  regard- 
less of  ])itch.  Under  such  circumstances  the  previously  published 
work  with  ("1  .51'-2  must  be  regarded  as  an  illustration,  as  a  part  of  a 
much  larger  problem,  —  the  most  interesting  part,  it  is  true,  be- 
cause near  the  middle  of  the  scale,  but  after  all  only  a  part.  Thus  a 
room  may  have  great  re\erberation  for  soimds  of  low  pitch  and  very 
little  for  sounds  of  high  i)itch,  or  exactly  the  reverse;  or  a  room  may 
have  comparatively  great  reverberation  for  sounds  both  of  liigh  and 
of  low  pitch  and  very  little  for  sounds  near  the  middle  of  the  scale. 
In  other  words,  it  is  not  putting  it  too  strongly  to  say  that  a  room 
may  have  very  different  quality  in  different  registers,  as  different 
as  does  a  musical  instrument;  or,  if  the  room  is  to  be  used  for 
speaking  purposes,  it  may  have  different  degrees  of  excellence  or 
defect  for  a  whisper  and  for  the  full  rounded  tones  of  the  voice, 
different  for  a  woman's  voice  and  for  a  man's  —  facts  more  or  less 


VARIATION  IN  REVERBERATION  79 

well  recognized.  Not  to  leave  this  as  a  vague  generalization  the 
following  cases  may  be  cited.  Recently,  in  discussing  the  acoustics 
of  the  proposed  cathedral  of  southern  California  in  Los  Angeles 
with  Mr.  Maginnis,  its  architect,  and  the  writer,  Bishop  Conaty 
touched  on  this  jjoint  very  clearly.  After  discussing  the  general 
subject  with  more  than  the  usual  insight  and  experience,  possibly 
in  part  because  Catholic  churches  and  cathedrals  have  great  rever- 
beration, he  added  that  he  found  it  difficult  to  avoid  pitching  his 
voice  to  that  note  which  the  auditorium  most  prolongs  notwith- 
standing the  fact  that  he  found  tliis  the  worst  pitch  on  which  to 
speak.  This  brings  out,  perhaps  more  impressively  because  from 
practical  experience  instead  of  from  IIicoi('ti(:;il  considerations,  the 
two  truths  that  auditoriums  have  very  ditfcrent  reverberation  for 
different  pitches,  and  that  excessive  reverberation  is  a  great  hin- 
drance to  clearness  of  enunciation.  Another  incident  may  also  serve, 
that  of  a  church  near  Boston,  in  regard  to  which  the  writer  has  just 
been  consulted.  The  present  pastor,  in  describing  the  nature  of  its 
acoustical  defects,  stated  that  diff<M-ent  speakers  had  different  de- 
grees of  difficulty  in  making  themselves  heard;  that  he  had  no  diffi- 
culty, liaving  a  rut  her  liigh  pitched  voice;  but  that  the  candidate 
before  him,  with  a  louder  l)ut  mucli  lower  voice,  failed  of  the  ap- 
j)ointment  because  unable  to  make  himself  heard.  Practical  ex- 
perience of  the  difference  in  reverberation  with  variation  of  pitch 
is  not  unusual,  but  the  above  cases  are  rather  striking  examples. 
Corresponding  effects  are  not  infrequently  observed  in  halls  devoted 
to  music.  Its  observation  here,  however,  is  marked  in  the  rather 
complicated  general  effect.  Tlu-  full  discussion  of  this  belongs  to 
another  series  of  papers,  in  which  will  be  taken  up  the  subject  of  the 
acoustical  effects  or  conditions  that  are  desirable  for  nuisic  and  for 
speech.  AVhile  this  pha.se  of  the  subject  will  not  be  discussed  here 
at  length,  a  little  consideraticm  of  the  data  to  be  presented  will  show 
how  j)roiu)unct'd  thesi-  effects  may  l)e  and  how  important  in  the 
general  subject  of  architectural  acoustics. 

In  order  to  show  the  full  significance  of  this  extension  of  the  in- 
vestigation in  regard  to  reverberation,  it  is  necessary  to  point  out 
some  features  whieli  in  earlier  i)apers  wen-  not  especially  empha- 
sized.    Primarily  the  investigation  is  concerned  with  the  subject  of 


80  AK(  IHTi:(  Tri{Ai,  ACOrSTICS 

rfVi-rluTiitioii.  lliat  is  lo  say,  with  tlu-  suhji-cl  of  tli(>  continuation  of 
a  soiintl  ill  a  nioin  after  tlu-  sourco  lia.s  coasi'd.  The  iinnudiale  etl'oct 
of  revfrluTatioM  is  that  each  nolo,  if  it  he  music,  each  syllable  or 
l>art  of  a  syllal)lf.  if  it  l)e  speech.  coMliiiucs  its  soiiml  for  sonic  lime. 
and  i»y  its  prolonf,'at ion  overlaps  the  succeediuii'  notes  or  syllables, 
Itarnionionsly  or  inliarnioniously  in  nnisic,  and  in  speech  always 
towards  confusion.  In  the  case  of  .sjH'cch  it  i.s  inconceivable  that 
this  prolongation  of  I  lie  sound,  this  reverberation,  should  have  any 
other  effect  than  that  of  confusion  and  injury  to  the  clearness  of  the 
enunciation.  In  music,  on  the  other  hand,  reverberation,  unless  in 
excess,  has  a  distinct  and  i)ositi\('  advantage. 

Perhaps  this  will  be  made  more  clear,  or  at  least  more  easily 
realized  and  :ipi)re(iatcd,  if  we  take  a  concrete  example.  Given  a 
room  comparatively  empty,  with  hard  wall-surfaces,  for  example 
plaster  or  tile,  and  having  in  it  comparatively  little  furniture,  the 
amoimt  of  reverberation  for  the  sounds  of  about  the  middle  register 
of  the  double-bass  viol  and  for  the  sounds  of  the  middle  register  of 
the  violin  will  be  very  nearly  though  not  exactly  ecjual.  If,  how- 
ever, we  bring  into  the  room  a  quantity  of  elastic  felt  cushions, 
sufficient,  let  us  say.  to  acconunodate  a  normal  audience,  the  effect 
of  these  cushions,  the  audience  being  supposed  absent,  will  be  to 
diminish  very  much  the  reverberation  both  for  the  double-bass  viol 
and  for  tlu-  violin,  but  will  diminish  them  in  very  unc(|ual  amounts. 
The  reverberation  will  now  be  twice  as  great  for  the  double-bass  as 
for  the  violin.  If  an  audience  comes  into  the  room,  filling  up  the 
seats,  the  reverberation  will  be  reduced  still  rurlhcr  anil  in  a  still 
greater  disproportion,  so  that  with  an  audience  entirely  filling  the 
room  the  reverberation  for  the  violin  will  be  less  than  one-third  that 
for  the  double-bass.  When  one  considers  that  a  difference  of  five 
per  cent  in  reverberation  is  a  matter  for  approval  or  disapproval  on 
the  part  of  musicians  of  critical  taste,  the  importance  of  considering 
these  facts  is  obvious. 

This  investigation,  nominally  in  regard  to  reverberation,  is  in 
realit\  laying  the  foundation  for  other  phases  of  the  problem.  It 
has  as  one  of  its  necessary  and  immediate  results  a  determination  of 
the  coefficient  of  absori)tion  of  sound  of  various  materials.  These 
coefficients  of  absorjjtion,  when  once  known,  enable  one  not  merely 


VARIATION  IN  REVERBERATION  81 

to  Ciilculalc  llu'  i)rolongation  of  tlu'  sound,  hul  also  to  calculate  the 
average  loudness  of  sustained  tones.  Thus  it  was  shown  in  one  of 
the  earlier  papers,  tliough  at  that  time  no  very  great  stress  was  laid 
on  it,  that  the  average  loudness  of  a  sound  in  a  room  is  proportional 
inversely  to  the  absorbing  powi-r  of  the  material  in  the  room.  There- 
fore the  data  which  are  being  presented,  covering  the  whole  range 
of  the  musical  scale,  enable  one  to  calculate  the  loudness  of  different 
notes  over  that  range,  and  make  it  possible  to  show  what  effect  the 
room  has  on  the  piano  or  the  orchestra  in  different  parts  of  the 
register. 

'I'o  illustrate  this  by  the  example  above  cited,  if  the  double-bass 
and  the  violin  produce  the  same  loudness  in  the  open  air,  in  the  bare 
room  with  hard  walls  both  would  l)e  reenforced  about  ec|ually.  The 
elastic  felt  brougiit  into  the  room  would  tieeidedly  diminish  this  re- 
enforcement  for  both  instruments.  It  would,  however,  exert  a  much 
more  pronounced  effect  in  the  way  of  diminishing  the  reenforcement 
for  the  violin  than  for  the  double-bass.  In  fact,  the  balance  will  be 
so  affected  that  it  will  rec|uire  two  violins  to  produce  the  same  vol- 
ume of  sound  as  does  one  double-bass.  The  audience  coming  into 
the  room  will  make  it  necessary  to  use  three  violins  to  a  double- 
bass  to  secure  the  same  balance  as  before. 

Both  cases  cited  above  are  only  broadly  illustrative.  As  a  matter 
of  fact  the  effect  of  the  room  and  the  effect  of  the  audience  in  the 
room  is  perceptibly  different  at  the  two  ends  of  the  register  of  the 
violin  and  of  the  double-bass  viol. 

'i'liere  is  still  a  third  effect,  which  must  be  considered  to  appre- 
ciate fully  the  i)ractical  significance  of  the  results  that  are  being 
presented.  This  is  the  effect  on  the  quality  of  a  sustained  tone. 
Every  musical  tone  is  composed  of  a  great  number  of  i)arlial  tones, 
the  predominating  one  being  taken  as  tlic  fundamental,  and  its 
pitch  as  the  ])iteh  of  the  sound.  The  otlier  partial  tt)nes  are  re- 
garded as  giving  (|ualily  or  color  to  the  fundamental.  The  musical 
quality  of  a  tone  depends  on  the  relatixc  intensities  of  the  overtones. 
It  has  been  customary,  at  least  nn  the  |)arl  of  pliysicists,  to  regard 
tin-  relative  intensities  of  the  overtones,  which  define  the  ((ualil\'  of 
the  soun<l,  as  de|)eniling  sim|)ly  on  the  sourer  from  which  the  sound 
originates.     Of  course,  jjrimarily,  this  is  true.     Nevertheless,  while 


8«  ARC  IHTECTURAL  ACOUSTICS 

llu-  source  drfitu-s  tlic  relative  intensities  of  the  issuing  sounds,  their 
actual  intensities  in  the  room  depend  not  merely  on  that,  but  also, 
and  to  a  surprising  degree,  on  the  room  itself.  Thus,  for  example, 
given  an  eight-foot  organ  pipe,  if  blown  in  an  empty  room,  such  as 
that  described  above,  the  overtones  would  be  j)ronounced.  If  ex- 
actly the  same  i)ipe  be  blown  with  the  same  wind  pressure  in  a  room 
in  which  the  seats  have  been  covered  with  the  elastic  felt,  the  first 
iiplKT  p;irlial  will  bear  to  the  fundamental  a  ratio  of  intensity 
dimiin'shed  over  40  per  cent,  the  second  upper  partial  a  ratio  to  the 
fundamental  diminished  in  the  same  per  cent,  the  third  upper 
l)artial  a  ratio  dimiuisiied  over  50  per  cent,  while  the  fourth  upper 
partial  will  bear  a  ratio  of  intensity  to  the  fundamental  diminished 
about  60  per  cent.  Quality  expressed  numericallj'  in  this  way 
probably  does  not  convey  a  very  vivid  impression  as  to  its  real 
effect.  It  may  signify  more  to  say  merely  that  the  change  in  quality 
is  very  pronounced  and  noticeable,  even  to  comparatively  imtrained 
ears.  On  the  other  hand,  if  one  were  to  try  the  experiment  with  a 
six-inch  instead  of  with  an  eight-foot  organ  pipe,  the  effect  of 
bringing  the  elastic  felt  cushions  into  the  room  would  be  to  increase 
the  relative  intensities  of  the  overtones,  and  thus  to  diminish  the 
purity  of  the  tone. 

All  tones  below  that  of  a  six-inch  organ  pipe  will  be  purified  by 
bringing  into  the  room  elastic  felt.  All  tones  above  and  including 
tiiat  i)itch  will  be  rendered  less  pure.  The  effect  of  an  audience 
coming  into  a  room  is  still  different.  Assuming  that  the  audience 
hii-s  filled  the  room  and  so  covered  all  the  elastic  felt  cushions,  the 
effect  of  the  audience  is  to  purify  all  tones  up  to  violin  C4  512,  and 
to  \ia\c  very  little  effect  on  all  tones  from  that  pitch  upward.  On 
very  low  tones  the  effect  of  the  audience  in  the  room  is  more  pro- 
nounced. For  example,  again  take  Ci  64,  the  effect  of  the  audience 
will  be  to  diminish  its  first  overtone  about  60  per  cent  relative  to 
the  fimdamental  and  its  second  overtone  over  75  per  cent. 

The  effect  of  the  material  used  in  the  construction  of  a  room,  and 
the  contained  furniture,  in  altering  the  relative  intensities  of  the 
fundamental  and  the  overtones,  is  to  improve  or  injure  its  quality 
according  to  circumstances.  It  may  be,  of  course,  that  the  tone 
desired  is  a  very  pure  one,  or  it  may  be  that  what  is  wanted  is  a 


VARIATION  IN  REVERBERATION  83 

tone  with  pronounced  upi)er  purtials.  Take,  for  example,  the 
"night  horn"  stop  in  a  pipe  organ.  This  is  intended  to  have  a  very 
pure  tone.  The  room  in  contributing  to  its  purity  would  improve 
its  quality.  On  the  other  liand,  the  mixture  stop  in  a  pipe  organ  is 
intended  to  have  very  pronounced  overtones.  In  fact  to  tliis  end 
not  one  but  several  pipes  are  sounded  at  once.  The  effect  of  the 
above  room  to  emphasize  the  fundamental  and  to  wipe  out  the 
overtones  would  be  in  opposition  to  the  original  design  of  the  stoj). 
To  determine  what  balance  is  desirable  nuist  lie  of  course  with  the 
musicians.  The  only  object  of  the  present  series  of  papers  is  to 
point  out  the  fundamental  facts,  and  that  our  conditions  may  be 
varied  in  order  to  attain  any  desired  end.  One  great  thing  needed 
is  that  the  judgment  of  the  nuisical  authorities  should  be  gathered 
in  an  available  form;  but  that  is  another  problem,  and  tlie  above 
bare  outline  is  intended  only  to  indicate  the  importance  of  extend- 
ing the  work  to  I  lie  whole  nmgc  of  the  musical  scale,  —  the  work 
undertaken  in  the  jjresent  paper. 

The  method  |)uisu('(l  in  these  exjK'riments  is  not  very  unlike  thai 
followed  in  the  previous  experiments  with  C4  51'-2.  It  diti'ers  in  minor 
detail.  l)ul  to  explain  these  details  would  involve  a  great  deal  of 
repetition  which  the  modifications  in  the  method  are  not  of  sufficient 
importance  to  justify. 

Rroadly,  the  procedure  consists  first  in  the  determination  of  the 
rate  of  emission  of  the  sound  of  an  organ  pipe  for  each  note  to  be 
investigated.  This  consists  in  determining  the  durations  of  au<libil- 
ity  after  the  cessation  of  two  sounds,  one  having  four  or  more,  but 
a  known  nmlliple,  times  the  intensity  of  the  other.  From  these 
results  it  is  possible  to  determine  the  rate  of  emission  by  the  pipes, 
each  in  terms  of  the  iiiinimum  audibility  for  tliat  i)articular  tone. 
The  a])paratus  used  in  tliis  part  of  tlie  experiment  is  shown  in  Fig.  1. 
Four  small  organs  were  lixed  at  a  minimum  distance  of  five  meters 
apart.  It  was  necessary  to  phu'c  tlicm  at  this  great  distance  ajKirl 
because,  as  already  pointed  out,  if  I'iaced  near  each  other  the  four 
sounded  logctlicr  do  not,  <'iiiit  lour  times  the  sound  emitted  by  one. 
This  wide  separation  was  particularly  necessary  for  the  large  pipe.-- 
and  the  low  tones;  a  very  Tuueh  less  .separation  would  have  .served 
the  i)urpose  in  the  ease  of  the  high  tones. 


84 


Al{<  MIIKC  TIUAL  .U  OUSTICS 


From  the  point  wIuti-  tlu-  four  tuln's  Ii-iulinj?  to  the  sinall  organs 
nuH't.  a  snp!)ly  piix-  ran.  as  sliown  on  the  drawing,  to  an  air  reservoir 
in  the  room  l»elo\v.  This  was  f<"(l  from  an  ek-ctrieally  driven  blower 
at  the  far  end  of  tla-  l)uihling.  Ilu'  clironograph  was  in  another 
room.     'I'lie  exi).riinriit>  with  liiis  a|jparatus.  hke  the  experiments 


^ZM' 


Fig.  1 


lierelofore  recorded,  were  carried  out  at  niglit  between  twelve  and 
five  o'clock. 

The  rate  of  emission  of  sound  by  the  several  pipes  having  been 
determined,  the  next  work  was  the  determination  of  the  coefficients 
of  al)sorption.  Tlie  methods  employed  having  already  been  suffi- 
ciently descriheil,  only  results  will  be  given. 

In  the  very  nature  of  the  problem  the  most  important  data  is  the 
absorption  coefficient  of  an  audience,  and  the  determination  of  this 
wjis  the  first  task  undertaken.  By  means  of  a  lecture  on  one  of 
the  recent  developments  of  i)hysics,  an  audience  was  enveigled  into 
attending,  and  at  the  end  of  the  lecture  requested  to  remain  for  the 
experiment.  In  this  attempt  the  effort  was  made  to  determine  the 
coefficients  for  the  five  octaves  from  C2 128  to  Ce  2048,  including 


VARIATION  IN  REVEIUJKHATION  85 

notes  E  and  (i  in  cucli  octave.  For  several  reasons  the  experiment 
was  not  a  success.  A  threatening'  tliuiider  storm  made  the  audience 
a  small  one,  and  tiie  siiilriness  of  the  almospliere  made  open  win- 
dows necessary,  while  the  attempt  to  cover  so  many  notes,  thirteen 
in  all,  prolonfi;ed  the  experiment  beyond  the  endurance  of  the  audi- 
ence. While  this  experiment  failed,  another  the  following  summer 
was  more  successful.  In  the  year  that  had  elapsed  the  necessity  of 
carrying  the  investigation  further  than  the  limits  intended  became 
evident,  and  now  the  experiment  was  carried  from  Ci  64  to  C7  4()()(), 
but  including  (mly  the  C'  notes,  .seven  notes  in  all.  Moreover, 
bearing  in  mind  the  experiences  of  the  previous  sununer,  il  was 
recognized  that  even  seven  notes  would  come  dangerously  near  over- 
taxing the  patience  of  the  audience.  Inasmuch  as  the  coefficient 
of  absorjjtion  for  ("4  ol'i  had  already  been  determined  six  years  be- 
fore in  the  investigations  mentioned,  the  coefficient  for  this  note 
was  not  redetermined.  The  experiment  was  therefore  carried  out 
for  the  lower  three  and  tiie  upper  three  notes  of  the  seven.  The 
audience,  on  the  night  of  tiiis  experiment,  was  much  larger  than 
that  whicli  came  the  previous  sununer,  the  night  was  a  more  com- 
forliil)l<'  one,  and  it  was  ])ossii)le  to  close  the  windows  during  (lie 
experiment.  'IMie  conditions  were  thus  fairly  satisfactory.  In  order 
to  get  as  nuich  data  as  possible  and  in  as  short  a  time,  there  were 
nine  observers  stationed  at  difl'ereni  points  in  the  room.  These  ob- 
servers, whose  kimlness  antl  skill  it  is  a  pleasure  to  acknowledge, 
had  prepared  themselves  by  i)revious  ])ractice  for  this  one  experi- 
ment. As  in  tlie  work  of  six  years  ago,  the  writer's  key  controlled 
the  organ  |)ipes  and  started  the  chronograph,  the  writer  and  the 
other  observers  each  had  a  key  which  was  connecteil  with  the 
chronograph  to  reectid  I  lie  cessation  of  audibilit_\'  of  the  sound.  The 
results  of  the  exijciiment  are  shown  on  the  lower  curve  in  Fig.  '2. 
This  curve  gives  the  coeilicient  of  al)sorption  ])er  ])erson.  It  is  to 
be  ob.served  that  one  of  the  points  fall>  clearly  otV  the  smooth  curve 
drawn  through  the  other  points.  The  observations  on  which  this 
point  i>  l)ased  were,  liowexci'.  inncli  (li>tinli<il  by  a  street  car  p;iss- 
ing  not  far  from  the  building,  and  the  dei)arture  of  tlii>  observation 
from  the  ciu-ve  does  not  indicate  a  real  deparlun-  in  the  coefHcient 
nor  should  it  cast  nuich  doubt  on  the  ri'>t  of  the  work,  in  view  of  the 


8G 


ARCHITEC  TURAL  ACOUSTICS 


circumstances  under  whicli  it  was  secured.  Counteracting  the  per- 
haps liad  impression  whicii  this  point  may  give,  it  is  a  considerable 
satisfaction  to  note  how  accurately   tin-   point  for  C4  512,  deter- 


1.0 

.« 

/ 

.H 

/ 

/ 

.7 

/ 

.6 

/ 

.6 

/ 

A 

.4 

1 

/ 

.3 

/ 

.2 

I 

.1 

c, 


c. 


c, 


c. 


c. 


c. 


Fig.  2.  The  absorbing  power  of  an  audience  for  Jifferent 
notes.  The  lower  curve  represents  the  absorbing  power 
of  an  audience  per  person.  The  upper  curve  represents 
the  absorbing  power  of  an  audience  per  square  meter 
as  ordinarily  seated.  The  vertical  ordinates  are  ex- 
pressed in  terms  of  total  absorption  by  a  square  meter 
of  surface.  For  the  upper  curve  the  ordinates  are  thus 
the  ordinary  coefficients  of  absorption.  The  several 
notes  are  at  octave  intervals,  as  follows:  Ci64,  GHS, 
Ci  (middle  C)  456,  C,51i.  C61W4,  C62048,  C7409G. 


mined  six  years  before  by  a  different  set  of  observers,  falls  on  the 
smooth  curve  through  the  remaining  points.  In  the  audience  on 
whicii  these  observations   were  taken   there   were  77  women  and 


\ARIATI()X  IX  REVP:RBERATI()X  87 

105  iiu'ii.  Tlic  coiirtt'sy  of  tin-  uuclience  in  remaining  for  the  ex- 
periment iiiid  I  he  really  remiirkal)le  silence  wliich  they  maintained 
is  gratefully  acknowledgeil. 

'I'he  curve  above  discussed  is  that  for  the  average  j)erson  in  an 
audience.  An  interesting  form  in  which  to  throw  the  results  is  to 
regard  the  audience  as  one  side  of  a  room.  We  may  then  look  at  it 
as  an  extended  absorbing  suriace,  and  determine  the  coefficient  per 
square  meter.  Worked  out  on  this  basis  the  absorption  coefficient 
is  indicated  in  the  higher  curve.  It  is  merely  the  lower  curve  nudti- 
plied  by  a  nunil)er  which  expresses  the  average  number  of  people 
per  s(juare  meter.  It  is  interesting  to  note  that  the  coefficient  of 
absorption  is  about  the  same  from  C4  5^2  up,  indicating  over  that 
range  nearly  complete  absorption.  Below  that  point  there  is  a  very 
great  falling  off',  down  to  L\  04.  The  curve  is  such  as  to  permit  of 
an  extrapolation  indicative  of  even  le.ss  absorption  and  consequently 
greater  reverberation  for  tiic  still  lower  notes.  Wilhout  entering 
into  an  elaborate  discussion  of  this  curve,  two  points  may  be  noted 
as  i)articularly  interesting.  The  first  is  the  nearly  complete  absorp- 
tion for  the  higher  notes,  a  result  which  at  first  sight,  seems  a  little 
inconsisteiil  with  the  roults  which  will  be  shown  later  on  in  con- 
nection with  the  al)sorptioii  i>.v  felt.  The  inconsistency,  however, 
is  only  apparent.  The  greater  absor])fion  shown  by  an  audience 
than  that  shown  by  thick  fell  arises  from  the  fact  that  the  surface 
of  the  audience  is  irregular  and  does  not  result  in  a  single  reflection, 
but  |)r()bably,  for  a  very  large  ])ortion  of  the  sound,  of  nudtiplt^  re- 
fli'clion  before  it  finally  euiergi's.  The  physical  conditions  are  such 
that  they  ol)viously  do  not  admit  of  analytic  expression,  but  the 
explanation  of  the  great  absorption  by  an  extended  audience  sur- 
face is  not  (liliicull  In  nndiTslaiid.  In  addition  to  the  aboxc  lliere 
is  another  i)artial  explanation  which  contributes  to  the  results, 
'i'he  felt  forms  a  perfectly  continuous  niediuni.  and  therefore  offers 
a  comparativi'ly  rigid  rellecting  surface.  Tlie  comparatively  light, 
thin,  and  porous  nature  of  the  clothing  of  women,  ])erhaps  more 
than  of  men,  contrilmtes  to  the  gi'eat  ai>M>r|)linn  of  the  high  notes. 

'I'he  next  ex|)erinu'nt.  taking  them  up  <'hronologically,  and  jmt- 
hajjs  next  even  from  the  standi)oint  of  interest,  w;us  in  regard  to  a 
brick  wall-surface.   This  expiriun-nt  wjis  carried  out  in  the  constant- 


88 


AUC  nil  KCTURAL  ACOUSTICS 


(«-miMTaliirf  rcHun  iiu-nlioiu-tl  in  tin-  previous  papers.  The  arrango- 
nu'iit  of  ai)paralus  is  sliown  in  Fig.  .'?,  wliere  the  air  re.servoir  in  the 
room  above  is  sliown  in  dotted  Hnes.  In  many  respects  theconstant- 
tenip«'rature  room  offered  admirable  conditions  for  the  experiment. 


,»f.-.-.is:\i.if-"» 


f^xnU  If  »^AWt  tT.'.'.^.-i  i%«'iv.%v»  4 


D" 


Its  jjosition  in  the  center  of  the  building  and  its  depth  underground 
made  it  comparatively  free  from  outside  disturbing  noises,  —  so 
much  so  that  it  was  possible  to  experiment  in  this  room  in  the  earlier 
parts  of  the  evening,  although  not,  of  course,  when  any  one  else  was 
at  work  in  the  building.     While  it  posses.ses  these  advantages,  its 


VARIATION  IN   REVERBERATION 


89 


arched  ceiling,  by  jjlaciiig  it  in  tlie  category  of  special  cases,  makes 
extra  precaution  necessary.  Fortunately,  at  the  beginning  of  the 
experiment  the  walls  were  uni)ainfe(l.     Tender  these  conditions  its 

.10 
.09 
.08 
.07 
.06 
.05 
.04 
.03 
.02 
.01 


Z^ZZ 


c. 


c. 


c, 


Fiii.  \.  The  absorbing  power  of  a.  4.5  em.  lliiek  brick  wall. 
Till'  upper  curve  repre.seiils  the  ulisorliiiif;  power  of  an 
iiiipaiiited  brick  .surface.  The  bricks  were  hard  but  not 
(jlazeil,  and  wire  set  in  cement.  The  hnver  curve  repre- 
sents the  absi>rl)iiif;  power  of  the  same  surface  painted 
with  two  coats  of  oil  paint.  The  difference  between 
the  two  curves  reprcsinls  the  absorption  due  to  the 
porosity  of  the  bricks.  In  small  part,  but  probably  only 
in  snuill  part,  the  dilference  is  due  to  diirertucc  in  super- 
ficial smoothness.    Ct  (middle  C)  iUU. 


coefficient  of  absorption  for  difVerent  notes  was  delerniined.  It  was 
then  painted  with  an  oil  paint,  two  coats,  and  its  coefficient  of  ab- 
sorption redetermined.     The  I  wo  curves  are  shown  in  I'ig.  \.     The 


<)()  ARrinTF.f'TrRAT,  vroT'STirs 

upiHT  curve  is  for  the  unpainted  brick;  the  lower  curve  is  that  ob- 
tained after  the  walls  were  painted.  The  difference  between  the 
two  curves  would,  if  plotted  alone,  be  the  curve  of  absorption  due 
to  the  j)orosity  of  the  brick.  It  may  seem,  perhaps,  that  the  i)aint 
in  covering  the  bare  brick  wall  made  a  smoother  surface,  and  the 
difference  between  the  two  results  might  be  due  in  part  to  le.ss  sur- 
face friction.  ()f  course  this  is  a  factor,  but  that  it  is  an  exceedingly 
small  factor  will  be  shown  later  in  the  discussion  of  the  results  on 
the  absorption  of  sound  by  other  bodies.  The  absorption  of  the 
sounil  after  the  walls  are  painted  is,  of  course,  due  to  the  yielding  of 
the  walls  under  the  vibration,  to  the  sound  actually  transmitted 
bodily  by  the  walls,  and  to  the  absorj)tion  in  the  process  of  trans- 
mission. It  is  necessary  to  call  attention  to  the  fact  that  the  vertical 
ordinates  are  here  magnified  tenfold  over  the  ordinates  shown  in  tlie 
last  curve. 

The  next  experiment  was  on  the  determination  of  the  absorption 
of  sound  by  wood  sheathing.  It  is  not  an  easy  matter  to  find  con- 
ditions suitable  for  this  experiment.  The  room  in  which  the  absorp- 
tion by  wood  sheathing  was  determined  in  the  earlier  experiments 
was  not  available  for  these.  It  was  available  then  only  because  the 
building  was  new  and  empty.  When  these  more  elaborate  experi- 
ments were  under  way  the  room  had  become  occupied,  and  in  a 
manner  that  did  not  admit  of  its  being  cleared.  Quite  a  little  search- 
ing in  the  neighborhood  of  Boston  failed  to  discover  an  entirely  suit- 
able room.  The  best  one  available  adjoined  a  night  lunch  room. 
The  night  lunch  was  bought  out  for  a  couple  of  nights,  and  the  ex- 
periment was  tried.  The  work  of  both  nights  was  much  disturbed. 
'J'he  traffic  jjast  the  building  did  not  stop  until  nearly  two  o'clock, 
and  began  again  about  four.  The  interest  of  those  passing  by  on 
foot  throughout  the  night,  and  the  necessity  of  repeated  explana- 
tions to  the  police,  greatly  interfered  with  the  work.  This  detailed 
statement  of  the  conditions  under  which  the  experiment  was  tried 
is  made  by  way  of  explanation  of  the  irregularity  of  the  observa- 
tions recorded  on  the  curve,  and  of  the  failure  to  carry  this  particular 
line  of  work  further.  The  first  night  seven  points  were  obtained  for 
the  seven  notes  Ci  64  to  C7  4096.  This  work  was  done  by  means 
of  a  portable  apparatus  shown  in  Fig.  5.     The  reduction  of  these 


VARIATION  IN  REVERBERATION 


91 


results  on  the  following  day  showed  variations  indicative  of  maxima 
and  minima,  which  to  be  accurately  located  would  require  the  de- 


Kio.  i 


terminal  ion  of  iuliTnu-dialc  i)(>inls.     Tin-  e.\]H'rinitnl  Llic  l'i)llo\ving 
niglil  was  by  means  of  the  organ  shown  in  Fig.  G,  and  points  were 


92 


AIU  HITK( "irRAL  ACOUSTICS 


dt'leniiiiu'd  for  the  K  aiul  G  noU's  in  each  octave  between  Cj  l'-28  and 
Ce  2048.  Oilier  points  would  have  been  determined,  but  time  did 
not  iMTiiiit .  It  is  obvious  that  the  intermediate  points  in  the  lower  and 


Fig.  6 


in  the  higher  octave  were  desirable,  but  no  pipes  were  to  be  had  on 
such  short  notice  for  this  part  of  the  range,  and  in  their  absence  the 
data  could  not  be  obtained.  In  the  diagram,  Fig.  7,  the  points  lying 
on  the  vertical  lines  were  determined  the  first  night.     The  points 


VARIATIOX  IN  REVERBERATIOX 


93 


lying  between  the  vertical  lines  were  determined  the  second  night. 
The  accuracy  with  which  these  points  fall  on  a  smooth  curve  is 


.12 
.U 

.10 
.09 
.08 
.07 
.06 
.06 
.04 
.03 
.02 
.01 


/  •  \ 

/  \* 


C, 


c. 


c, 


c. 


c. 


c, 


Flo.  7.  Till'  iil)sorl)iii>'  power  of  wood  .shoalliinK.  two  centi- 
nifttT.s  thick,  Nortli  Curoliim  pine.  Tlic  ohservntions 
were  imiili'  uikIit  wry  unsiiiliiblc  comlilions.  The 
Hl)Sorptioii  is  hrrc  ilui-  almost  wholly  to  yirliliiij;  of  tht- 
shrnthin^'  us  a  wholr.  thr  surface  Ix'iii);  shellaeked, 
sinuoth.  and  iioii-poroiis.  The  rurve  shows  one  point 
of  resonance-  within  the  ran^je  tested,  and  the  proh- 
nbility  of  another  point  of  resonance  alM>ve.  It  is  not 
possible  now  to  learn  as  much  in  regard  to  the  franiinK 
and  arrangement  of  lh<-  st milling;  in  the  particular  room 
tested  as  is  desirable,    d  iniiddle  ("I  ioU. 


94  AH(  lIITKC'TrRAL  ACOUSTICS 

prrliaps  all  that  could  he  cxpi-cted  in  view  of  the  difficulty  under 
which  the  observations  were  conducted  and  the  limited  time  avail- 
able. One  jKiint  in  jjarticular  falls  far  off  from  this  curve,  the  point 
for  C3  iod,  by  an  amount  which  is,  to  say  the  least,  serious,  and 
which  can  be  justified  only  by  the  conditions  under  which  the  work 
was  done.  The  general  trend  of  the  curve  seems,  however,  estab- 
lished beyond  ri'asoiial)le  doubt.  It  is  interesting  to  note  that  there 
is  one  point  of  maximum  absorption,  which  is  due  to  resonance  be- 
tween I  lie  \v;ill>  and  I  lie  sound,  and  that  this  point  of  maximum 
absorjition  lies  in  the  lower  i)art.  though  not  in  the  lowest  part,  of 
the  range  of  pitch  testeil.  It  would  have  been  interesting  to  deter- 
mine, hail  the  time  and  facilities  permitted,  the  shape  of  the  curve 
beyond  C7  4096,  and  to  see  if  it  rises  indefinitely,  or  shows,  as  is  far 
more  likely,  a  succession  of  maxima.  The  scale  employed  in  this 
curve  is  the  same  as  that  employed  in  the  diagram  of  the  unpainted 
and  painted  wall-surfaces.  It  may  perhaps  be  noted  in  this  con- 
nection that  at  the  very  least  the  absorption  is  four  times  that  of 
painted  brick  walls. 

TliefX])erinu'nt  was  then  directed  to  the  determination  of  the  ab- 
sorption of  sound  by  cushions,  and  for  this  purpose  return  was  made 
to  the  constant-temperature  room.  Working  in  the  manner  indicated 
in  tlie  earlier  papers  for  substances  which  could  be  carried  in  and 
out  of  a  room,  the  curves  represented  in  Fig.  8  were  obtained. 
Curve  1  shows  the  absorption  coefficient  for  the  Sanders  Theatre 
cushions,  with  which  the  whole  investigation  was  begun  ten  years 
ago.  These  cushions  were  of  a  particularly  open  grade  of  packing, 
a  sort  of  wiry  grass  or  vegetable  fiber.  They  were  covered  with 
canviis  ticking,  and  that  in  turn  with  a  very  thin  cloth  covering. 
Curve  "2  is  for  cushions  borrowed  from  the  Phillips  Brooks  House. 
They  were  of  a  high  grade,  filled  with  long  curly  hair,  and  covered 
with  canvas  ticking,  which  was  in  turn  covered  by  a  long  nap  plush. 
Curve  3  is  for  the  cushions  of  Ajipleton  Chapel,  hair  covered  with  a 
leatherette,  and  showing  a  sharper  maximum  and  a  more  rapid 
diminution  in  absorption  for  the  higher  frequencies,  as  would  be 
expected  under  such  conditions.  Curve  4  is  probably  the  most 
interesting,  because  for  more  standard  commercial  conditions.  It 
is  the  curve  for  elastic  felt  cushions  as  made  by  Sperry  and  Beale. 


VARIATION  IN  REVERBERATION 


95 


It  is  to  be  observed  thai  all  four  curves  fall  off  for  the  liiglier  fre- 
quencies, all  show  a  inaxiniuin  Kx-ated  within  an  octave,  and  three 


1.0 


A 

\ 

// 

^f 

\ 

4 

^ 

\ 

\ 

'^ 

/ 

I' 

\ 

\ 

\\ 

/    / 

J 

V 

\ 

\ 

-A 

7 

\ 

/> 

r 

\ 

^ 

c, 


c, 


c. 


c. 


c, 


Fig.  8.  The  ahsorhiiij;  power  of  cushions.  Curve  1  is 
for  "Sanders  Tliealre"  cushions  of  wiry  vejjetuble 
6bcr.  covered  with  canvas  tickin;;  and  a  tliin  cloth. 
Curve  i  is  for  "Hrooks  House"  cushions  of  long  hair, 
covered  with  the  same  kind  of  tickinjj  and  phish. 
Curve  3  is  for  ".Vpplelon  Chapel"  cushions  of  hair, 
covered  with  ticking  and  a  thin  leatherette.  Curve  4 
is  for  the  elastic  felt  cushions  of  coninuTce.  of  elastic 
cotton.  covere<l  with  ticking  and  short  nap  plush.  The 
ab.sorl)ing  power  is  per  square  meter  of  surface. 
Cj  (middle  C)  2JCi. 

of  the  curves  show  a  curious  hiiinp  in  I  he  second  ocla\i>.  This 
break  in  the  curve  is  a  genuine  pliciioiiienon,  as  it  was  tested  time 
after  time.    It  is  j)erhai)s  <lue  to  a  .secondary  resonance,  and  it  is  to 


96 


AH(  IIITEC'l  URAL  ACOUSTICS 


be  observed  that  it  is  the  more  i)ronoimced  in  those  curves  that  have 
tlu'  sharper  resonanee  in  their  jirincipal  maxima. 

Observations  were  llien  obtained  on  unupholstered  chairs  and 
settees.  The  result  for  chairs  is  shown  in  Fig.  10.  This  curve  gives 
the  absorption  coefficient  per  single  chair.  The  effect  was  surpris- 
ingly small;  in  fact,  when  the  floor  of  the  constant-temperature 
room  was  entirely  covered  with  the  chairs  sjxiced  at  usual  seating 
distances,  the  effect  on  the  reverberation  in  the  room  was  exceed- 


FiG.  9 


ingly  slight.  The  fact  that  it  was  so  slight  and  the  consequent  dif- 
ficulty in  mejisuring  the  coefficient  is  a  partial  explanation  of  the 
variation  of  the  results  as  indicated  in  the  figure.  Nevertheless  it 
is  probable  that  the  variations  there  indicated  have  some  real  basis, 
for  a  repetition  of  the  work  showed  the  points  again  falling  above 
and  below  the  line  as  in  tht-  first  experiment.  The  amount  that 
these  fell  above  and  below  the  line  was  difficult  to  determine,  and 
the  number  of  points  along  the  curve  were  too  few  to  justify  at- 
tempting to  follow  their  values  by  the  line.  In  fact  the  line  is  drawn 
on  the  diagram  merely  to  indicate  in  a  general  way  the  fact  that  the 
coefficient  of  absorption  is  nearly  the  same  over  the  whole  range.  A 
varying  resonance  phenomenon  was  unquestionably  present,  but  so 
small  as  to  be  negligible;  and  in  fact  the  whole  absorption  by  the 
chairs  is  an  exceedingly  small  factor.  The  chair  was  of  ash,  and  its 
type  is  shown  in  tlie  accompanying  sketch.  Fig.  9. 

The  results  of  the  observations  on  settees  is  shown  in  Fig.  11. 
Those  plotted  are  the  coefficients  per  single  seat,  there  being  five 
seats  to  the  settee.    The  settees  were  placed  at  the  customary  dis- 


VARIATION  IN  RK\'KRBERATK)N 


97 


I  'r  c 


tiince.  Here  again  the  {)rinfipal  interest  attaches  to  the  fact  that 
the  coefficient  of  absorption  is  so  exceedingly  small  that  the  total 
effect  on  the  reverberation  is  hardly  noticeable.  Here  also  the 
plotted  results  do  not  fall  on  the  line  drawn,  and  the  departure  is 
.03 


.02 


.01 


c.        c,        a        c.        C:        c.       c, 

Fig.  10.  The  absorbing  power  of  ash  chairs  shown  in  Fig.  9. 

(hie  i)robably  to  some  slight  resonance.  The  magnitude  of  the  de- 
parture, however,  could  not  be  determined  with  accuracy  because  of 
the  small  magnitude  of  the  total  absorption  coefficient.  For  these 
reasons  and  because  the  number  of  points  was  insufficient,  no  at- 

.03 


.02 


.01 


: ~  ' 


C. 


C, 


c. 


c> 


c. 


c, 


Fig.  11.  The  ab.sorbiiig  power  of  ash  settees  shown  in 
Fig.  9.  The  absorption  is  per  single  scat,  the  settee 
as  shown  seating  five. 

tem])t  was  inade  lo  diMW  I  he  cuinc  throiij,'!)  the  plotted  points,  but 
mer("ly  to  indicate  a  plotted  tendency.  The  settees  were  of  ash, 
and  their  general  style  is  shown  in  the  sketch. 

An  investigation  was  then  begun  in  regard  U>  I  In-  nature  of  I  lie 
process  of  absorption  of  .sound.  The  material  chosen  for  this  work 
was  a  \rvy  durable  grade  of  i'lil.  wliicli.  as  the  mamifacturers 
claimed,  was  all  wool.  Kveii  a  casual  examination  of  its  texture 
makes  it  difliciilt  to  believe  that  it  is  all  wool.     It  has.  however,  the 


08  AU(  Iiri'ECTURAL  ACOUSTICS 

advantage  of  hcing  porous,  flexible,  and  very  durable.  Almost  con- 
stant handling  for  several  years  has  apparently  not  greatly  changed 
its  consistency.  It  is  to  be  noted  that  this  felt  is  not  that  mentioned 
in  the  papers  of  six  years  ago.  That  felt  was  of  lime-treated  cow's 
hair,  the  kind  used  in  packing  steam  pipes.  It  was  very  much  cheai)er 
in  i)rice.  but  stood  little  handling  before  disintegrating.  The  felt 
emi)loyed  in  these  experiments  comes  in  sheets  of  various  thick- 
nesses, the  thickness  here  employed  being  about  1.1  cm. 

The  coefficient  of  absorption  of  a  single  layer  of  felt  was  measured 
for  the  notes  from  Cj  (>4  to  C-  4096  at  octave  intervals.  The  experi- 
ment was  repeated  for  two  layers,  one  on  top  of  the  other,  then  for 
three,  and  so  on  up  to  six  thicknesses  of  felt.  Because  the  greater 
thicknesses  presented  an  area  on  the  edge  not  inconsiderable  in 
comparison  with  the  surface,  the  felt  was  surrounded  by  a  narrow 
wood  frame.  Tender  such  circumstances  it  was  safe  to  assume  that 
the  absorption  was  entirely  by  the  upper  surface  of  the  felt.  The 
experiment  was  repeated  a  great  many  times,  first  measuring  the 
coefficient  of  absorption  for  one  thickness  for  all  frequencies,  and 
then  checking  the  work  by  conducting  experiments  in  the  other 
order;  that  is,  measuring  the  absorption  by  one,  two,  three,  etc., 
thicknesses,  for  each  frequency.  The  mean  of  all  observations  is 
shown  in  Fig.  12  and  Fig.  13.  In  Fig.  12  the  variations  in  pitch  are 
plotted  as  abscissas,  as  in  previous  diagrams,  whereas  in  Fig.  13  the 
thicknesses  are  taken  as  abscissas.  The  special  object  of  the  second 
method  will  appear  later,  but  a  general  object  of  adopting  this 
method  of  plotting  is  as  follows: 

If  we  consider  Fig.  12,  for  example,  the  drawing  of  the  line  through 
any  one  .set  of  points  should  be  made  not  merely  to  best  fit  those 
points,  but  should  be  drawn  having  in  mind  the  fact  that  it,  as  a 
curve,  is  one  of  a  family  of  curves,  and  that  it  should  be  drawn  not 
merely  as  a  best  curve  through  its  own  points,  but  as  best  fits  the 
whole  set.  For  example,  in  Fig.  12  the  curve  for  four  thicknesses 
would  not  have  been  drawn  as  there  shown  if  drawn  simjjly  with 
reference  to  its  own  points.  It  would  have  been  drawn  directly 
through  the  points  for  Ci  64  and  C2  128.  Similarly  the  curve  for 
five  thicknesses  would  have  been  drawn  a  little  nearer  the  point  for 
C2 128,  and  above  instead  of  below  the  point  for  Ci  64.    Considering, 


VARIATION  IN  RE^TRBERATION 


99 


however,  the  whole  family  of  curves  and  recognizing  that  each  point 
is  not  without  some  error,  the  curves  as  drawn  are  more  nearly 
correct.    The  liest  method  of  reconciling  the  several  curves  to  each 

l.O 


.8 


.4 


/y 

^ 

/ 

// 

/  /4/ 

/ 

V 

// 

h\ 

/ 

\ 

^ 

/^ 

// 

1  r 

/ 

/ 

^  / 

7 

/l 

J 

/ 

y 

J 

y 

.2  ^ 


C. 


C, 


c. 


c. 


c. 


c, 


Fig.  12.  The  uhsorbiiig  power  of  fell  of  (liircrciit  thick- 
nesses. Kach  piece  of  felt  was  1.1  cm.  in  thickness. 
Curve  1  is  for  a  sint;l<'  I  hickncss,  curve  i  for  two  thick- 
nesses placed  one  on  top  of  tiie  other,  etc.  As  shown 
by  these  curves,  the  absorption  is  in  part  by  penetra- 
tion into  the  pores  of  the  felt,  in  part  by  a  yicKlin);  of 
the  mass  as  a  wliole.  Resonance  in  the  latter  process 
is  clearly  shown  by  a  maximum  shiftinj;  to  lower 
and  lower  pitch  with  increase  in  thickness  of  the  felt. 
Cj  (middle  C;  iJU. 

other  is  to  plot  two  diagram.s,  one  in  which  the  variations  in  i)itc]i 
arc  taken  as  ab.scissa  and  one  in  which  the  variations  in  thickness 
of  iVlt  are  taken  as  abscis.sas;   then  draw  through  the  points  the  best 


100  ARCHITKCTURAL  ACOUSTICS 

fitlinj;  curves  iind  avoraRO  flu>  com-spoiulinij  ordinate's  takt-ii  from 
I  lit-  curves  thus  drawn;  and  with  lliese  average  ordinates  redraw 
both  families  of  curves.  Tlie  points  shown  on  the  diagram  are  of 
course  the  original  residts  obtained  experimentally.  In  general 
they  fall  pretty  dose  to  the  curves,  although  at  times,  as  in  the 
j)oints  noted,  they  fall  rather  far  to  one  side. 

The  following  will  serve  to  present  the  points  of  particular  in- 
terest revealed  1).\  the  family  of  curves  in  Fig.  12,  where  the  absorp- 
tion by  the  several  thicknesses  is  j^lotted  against  pitch  for  abscissas. 
It  is  to  be  observed  that  a  single  thickness  scarcely  absorbs  the  sound 
from  the  eight,  four,  and  two-foot  organ  pipes,  Cj  64,  C2  l^S,  and 
C3  256,  and  tlial  its  al)sorption  increases  rapidly  for  the  next  two 
octaves,  after  which  it  remains  a  constant.  Two  thicknesses  absorb 
more  —  about  twice  as  nnich  -  for  the  lower  notes,  the  curve  rising 
more  rapidly,  passing  tliroiigii  a  maximum  between  C4  512  and 
Cs  1024,  and  then  falling  off  for  the  higher  notes.  The  same  is  true 
for  greater  thicknesses.  All  curves  show  a  maximvmi,  each  succeed- 
ing one  corresponding  to  a  little  lower  note.  The  maximum  for  six 
thicknesses  coincitles  pretty  closely  to  C4  512.  The  absorption  of 
the  sound  by  felt  may  be  ascribed  to  three  causes,  —  porosity  of 
slructure,  compression  of  the  felt  as  a  whole,  and  friction  on  the 
surface.  The  presence  of  the  maximum  must  be  ascribed  to  the 
second  of  these  causes,  the  compression  of  the  felt  as  a  whole.  As 
to  the  third  of  these  three  causes,  it  is  best  to  consult  the  curves  of 
the  next  figure. 

The  following  facts  are  rendered  particularly  evident  by  the 
curves  of  Fig.  13.  For  the  tones  emitted  by  the  eight-foot  organ 
pipe,  Ci  64,  the  absorption  of  the  sound  is  verj'  nearly  proportional 
to  the  thickness  of  the  felt  over  the  range  tested,  six  thicknesses, 
(i.6cm.  The  curves  for  notes  of  increasing  pitch  show  increasing 
value  for  the  coefficients  of  absorption.  They  all  show  that  were 
the  thickness  of  the  felt  sufficiently  great,  a  limit  would  be  ap- 
proached—  a  fact,  of  course,  self-evident  —  but  for  C5  1024  this 
thickness  was  reached  w-ithin  the  range  experimented  on;  and  of 
course  the  same  is  true  for  all  higher  notes,  Ce  2048  and  C7  4096. 
The  higher  the  note,  the  less  the  thickness  of  felt  necessary  to  pro- 
duce a  maximum  effect.    The  curves  of  Ci  64,  C2  128,  C3  256,  and 


VARIATION  IN  REVERBERATION 


101 


C4  512,  if  extended  backward,  would  pass  nearly  through  the  origin. 

This  indicates  that  for  at  least  notes  of  so  low  a  pitch  the  absorption 

l.O 


.2 


^ 

X 

rv 

J\ 

/^ 

J 

/ 

/ 

/ 

1 , 

r^ 

/ 

/ 

?. 

h 

/ 

/ ' 

/ 

y 

/ 

/ 

^ 

/ 

/ 

^/ 

^c, 

1 

//■ 

f  .^ 

4 

r 

1 

13  3  4  6  6 

Fig.  13.  The  absorbing  power  of  felt  of  different  tliick- 
nesscs.  The  data,  Fig.  M,  is  here  i)lotte<l  in  a  slightly 
different  manner  —  horizontally  on  plotted  increasing 
thickness  —  and  the  curves  are  for  notes  of  different 
frequency  at  octave  intervals  in  pitch.  Thus  plotted 
the  curves  show  the  necessary  thickness  of  felt  for 
practically  maxiniuni  efhcieney  in  absorbing  sound  of 
different  pitch.  These  curves  also  show  that  for  the 
lowest  tliree  notes  surface  friction  is  negligiljle,  at  leust 
in  comparison  with  the  other  factors.  For  the  liigh 
notes  one  thickness  of  felt  was  too  great  for  the  curves 
to  be  conclusive  in  regard  lo  this  point.  Ci  (middle 
C) 250. 

of  sound  would  be  ziTO,  or  nearly  zero,  for  zero  tliicknoss.     Since 
zero  thickness  would  leave  surface  effects,  the  argiuuent  leads  to 


lo-,'  ARCIIITKf  TrRAL  ACOUSTICS 

thi'  c-onclusion  that  surface  frictiuii  as  an  agent  in  the  absorption  of 
sound  is  of  small  importance.  The  curves  plotted  do  not  give  any 
evidence  in  lliis  respect  in  regard  to  the  Iiigher  notes,  €5 1024, 
Cs  ^048,  and  C7  409G. 

It  is  of  course  evident  that  tlie  above  data  do  not  by  any  means 
cover  all  the  ground  that  shoidd  be  covered.  It  is  highly  desirable 
that  data  should  be  accessii)le  for  glass  surfaces,  for  glazed  tile  sur- 
faces, for  plastered  and  inii)lastered  porous  tile,  for  plaster  on  wood 
lalh  and  plaster  on  wire  lath,  for  rugs  and  carpets;  but  even  with 
these  data  collected  the  job  would  be  by  no  means  comi)leted. 
What  is  wanted  is  not  merely  the  measurement  of  existing  material 
and  widl-surfaces,  but  an  investigation  of  all  the  po.ssibilities.  A 
concrete  case  will  perhaps  illustrate  this.  If  the  wall-surface  is  to 
be  of  wood,  there  enter  the  cjuestions  as  to  what  would  be  the  effect 
of  varying  the  material,  —  how  ash  differs  from  oak,  and  oak  from 
walnut  or  i)ine  or  whitewood;  what  is  the  effect  of  variations  in 
thickness;  what  the  effect  of  paneling;  what  is  the  effect  of  the 
spacing  of  the  furring  on  wliich  the  wood  sheathing  is  fastened.  If 
the  wall  is  to  be  plaster  on  latli,  there  arises  the  question  as  to  the 
difference  between  wood  lath  and  wire  lath,  between  the  mortar 
that  was  formerly  used  and  the  wall  of  today,  which  is  made  of  hard 
and  im])ervious  plaster.  What  is  the  effect  of  variations  in  thick- 
ness of  the  plaster  .^  What  is  the  effect  of  painting  the  jjlaster  in 
oil  or  in  water  colors  ?  What  is  the  effect  of  the  depth  of  the  air 
space  behind  the  plaster  ?  The  recent  efforts  at  fireproof  construc- 
tion have  resulted  in  the  use  of  harder  and  harder  wall-surfaces, 
and  great  reverberation  in  the  room,  and  in  many  cases  in  poorer 
acoustics.  Is  it  possible  to  devise  a  material  which  shall  satisfj'  the 
conditions  as  to  fireproof  qualities  and  yet  retain  the  excellence  of 
some  of  the  older  but  not  fireproof  rooms  ?  Or,  if  one  turns  to  the 
interior  furnishings,  what  type  of  chair  is  best,  what  form  of  cushions, 
or  what  form  of  upholstery  ':  There  are  many  forms  of  auditorium 
chairs  and  settees,  and  all  these  should  be  investigated  if  one  pro- 
poses to  apply  exact  calculation  to  the  problem.  These  are  some  of 
the  questions  that  have  arisen.  A  few  data  have  been  obtained 
looking  toward  the  answer  to  some  of  them.  The  difficulty  in  the 
way  of  the  prosecution  of  such  work  is  greater,  however,  than  ap- 


VARIATION  IN  REVKRHKRA'l'ION  103 

pears  at  first  sight,  the;  parliciilar  diiliciilties  being  of  opportunity 
and  of  expense.  It  is  difficult,  for  i'xanii)le,  to  find  rooms  wliose 
walls  are  in  large  measure  of  glass,  especially  when  one  bears  in 
mind  that  the  room  must  be  empty,  that  its  other  wall-surfaces 
must  be  of  a  substance  fully  investigated,  and  that  it  must  be  in  a 
location  admitting  of  quiet  work.  Or,  to  investigate  the  effect  of 
the  different  kinds  of  plaster  and  of  the  different  methods  of  plaster- 
ing, it  is  necessary  to  have  a  room,  preferably  an  underground  room, 
which  can  be  lined  and  relined.  The  constant-temperature  room 
which  is  now  available  for  the  experiments  is  not  a  room  suitable 
to  that  particular  investigation,  and  for  best  results  a  special  room 
should  be  constructed.  Moreover,  the  expense  of  plastering  and 
replastering  a  room  —  and  this  process,  to  arrive  at  anything  like 
a  general  solution  of  the  problem,  would  have  to  be  done  a  great 
many  times  —  would  be  very  great,  and  is  at  the  present  moment 
prohibitive.  A  little  data  along  some  of  these  lines  have  been  se- 
cured, but  not  at  all  in  final  form.  The  work  in  the  past  has  been 
largely  of  an  analytical  nature.  Could  the  investigation  take  the 
form  of  constructive  research,  and  lead  to  new  methods  and  greater 
possibilities,  it  would  be  taking  its  more  interesting  form. 

The  above  discussion  has  been  solely  with  reference  to  the  deter- 
mination of  the  coefficient  of  absorption  of  sound.  It  is  now  pro- 
posed to  discuss  the  question  of  the  apj)lication  of  these  coefficients 
to  the  calculation  of  reverl)eration.  In  the  first  series  of  papers, 
reverberation  was  defined  with  reference  to  C4  512  as  the  continua- 
tion of  the  sound  in  a  room  after  the  source  had  ceased,  the  initial 
intensity  of  the  sound  being  one  million  times  minimum  audible 
intensity.  It  is  debatable  whether  or  not  this  tlefinition  should  be 
extended  without  alteration  to  reverberation  for  other  notes  than 
C4  512.  There  is  a  good  deal  to  l)e  said  both  for  and  against  its 
retention.  The  whole,  however,  hinges  on  the  outcome  of  a  physi- 
ological or  psychological  inquiry  not  yet  in  such  shape  as  to  lead  to 
a  final  decision,  'llie  ([ucslion  is  therefore  held  in  abeyance,  and 
for  I  lie  lime  the  definition  is  retained. 

Retaining  the  defiiiilion,  I  lie  reverberation  for  any  pilch  can  lie 
calculated  bv  I  lie  foruinla 

a 


104  ARCHITECTURAL  ACOUSTICS 

where  V  is  the  vohiine  of  the  room,  A'  is  a  constant  depending  on 
the  initial  intensity,  and  a  is  the  total  absorbing  power  of  the  walls 
and  the  contained  material.     A'  and  V  are  the  same  for  all  pitch 


8 
8 
7 

Q 

5 

4 

3 

I 

2 

V 

1 

c, 


c. 


c. 


Fig.  14.  Curves  expressing  the  reverberation  in  the  large 
lecture-room  of  the  Jefferson  Physical  Laboratory  with 
(lower  curve)  and  without  (upper  curve)  an  audience. 
These  curves  express  in  seconds  the  duration  of  the 
residual  sound  in  the  room  after  the  cessation  of 
sources  producing  intensities  10'  times  minimum 
audible  intensity  for  each  note.  The  upper  curve  de- 
scribes acoustical  conditions  which  are  very  unsatis- 
factory, as  the  hall  is  to  be  used  for  speaking  purposes. 
The  lower  curve  describes  acoustically  satisfactory 
conditions.  Cs  (middle  C)  256. 

frequencies.  A  is  .164  for  an  initial  intensity  10^  times  minimum 
audible  intensity.  The  only  factor  that  varies  with  the  pitch  is  a, 
which  can  be  determined  from  the  data  given  above. 


VARIATION  IN  REVERBERATION  105 

In  illustration,  the  curves  in  the  accompanying  Fig.  1-t  give  the 
reverberation  in  the  large  lecture-room  of  the  Jefferson  Physical 
Laboratory.  The  upper  curve  defines  the  reverberation  in  the  room 
when  entirely  empty;  the  lower  curve  defines  this  reverberation  in 
the  same  room  with  an  audience  two-thirds  filling  the  roon).  The 
upper  curve  represents  a  condition  which  would  be  entirely  impracti- 
cal for  speaking  purposes;  the  lower  curve  represents  a  fairly  satis- 
factory condition. 


MELODY  AND  THE  ORIGIN  OF  THE  MUSICAL 

SCALE" 

In  the  vice-presidential  addresses  of  the  American  Association 
great  hititude  in  the  choice  of  subjects  is  allowed  and  taken,  but 
there  is,  I  believe,  no  precedent  for  choosing  the  review  of  a  book 
printed  fifty-five  years  before.  Helmlioltz'  Tonenemfinduiujen,  pro- 
duced by  a  masterful  knowledge  of  jjhysiology,  physics,  and  mathe- 
matics, and  a  scholar's  knowledge  of  the  literature  of  music,  has 
warded  off  all  essential  criticism  by  its  breadth,  completeness,  and 
wealth  of  detail.  Since  it  was  first  published  it  has  been  added  to 
by  the  author  from  time  to  time  in  successive  editions,  and  greatly 
bulwarked  by  the  scholarly  notes  and  appendices  of  its  translator, 
Dr.  Alexander  J.  Kllis.  Tlic  original  text  remains  unchanged,  and 
unchallenged,  ;xs  far  as  physicists  are  concerned,  in  all  important 
respects.  In  taking  exception  at  this  late  day  to  the  fundamental 
thesis  of  Tart  III,  I  derive  the  necessary  courage  from  the  fact  that 
should  such  exception  be  sustained,  it  will  serve  to  restore  to  its 
full  application  that  greater  and  more  original  contribution  of  Helm- 
holtz  which  he  included  in  Part  II.  Having  given  a  physical  and 
physiological  explanation  of  the  harmony  and  discord  of  simul- 
taneous sounds,  and,  therefore,  an  explanation  of  the  musical  scale 
as  used  in  modern  composition,  Ilelmholtz  was  met  by  an  apparent 
anachronism.  The  musical  scale,  identical  with  the  modern  musi- 
cal scak'  in  all  essentials,  antedated  by  its  use  in  single-jiart  melody 
the  invention  of  chordal  comi)osition,  or,  as  Ilelmholtz  expressed 
it,  preceded  all  experience  of  musical  harmony.  In  .seeking  an  ex- 
planation of  this  early  invention  of  the  musical  scale,  Ilelmholtz 
abandoned  his  most  notable  contribution,  and  relegated  liis  expla- 
nation of  harmony  and  discord  to  the  minor  service  of  explaining 
a  fortunate,  though  of  course  an  important  use  of  an  already  in- 
vented system  of  musical  notes.     The  explanation  of  the  original 

*  Vice-Presidential  .\ddress.  Section  B,  American  .\ssociBlion  for  tin-  .Vdvanccnicnl  of 
Science,  Chicago,  1907. 

107 


108  MELODY 

invention  of  the  musical  scale  and  its  use  in  single-part  music 
Ihrouph  the  classical  and  the  early  Christian  eras,  he  sought  for 
in  i)urely  aestlietic  considerations,  —  in  exactly  those  devices  from 
wliich  he  had  just  succeeded  in  rescuing  the  explanation  of  harmony 
and  discord. 

The  liunian  ear  consists  of  three  parts,  —  in  the  nomenclature 
of  anatomy,  of  the  outer,  niitldle,  and  inner  ear.  The  outer  and 
the  inner  ears  are  connected  by  a  series  of  three  small  bones  trav- 
ersing the  middle  ear  and  transmitting  the  vibrations  of  sound. 
'I'lie  inner  ear  is  a  peculiarly  shai)ed  cavity  in  one  of  the  hard  bones 
of  tlie  skull.  That  i)art  of  the  cavity  with  which  we  are  here  con- 
cerned is  a  long  passage  called  from  its  resemblance  to  the  interior 
of  a  snail  shell  the  cochlea.  The  cavity  has  two  windows  which  are 
closed  by  membranes.  It  is  to  the  uppermost  of  these  membranes 
that  the  train  of  three  small  bones,  reaching  from  the  drum  of  the 
outer  ear,  is  attached  at  its  inner  end.  It  is  to  this  upper  membrane, 
therefore,  tluit  tiio  vibration  is  communicated,  and  through  it  the 
\ibration  reaches  the  fluid  which  fills  the  inner  cavity.  As  the 
membrane  covering  tlie  ui)per  window  vibrates,  the  membrane 
covering  the  lower  window  yielding,  also  vibrates,  and  the  motion 
of  the  fluid  is  in  the  nature  of  a  slight  displacement  from  one  to 
the  other  window,  to  and  fro.  From  between  these  windows  a  dia- 
phragm, dividing  the  passageway,  extends  almost  the  whole  length 
of  the  cochlea.  This  diaphragm  is  composed  in  part  of  a  great 
number  of  very  fine  fibers  stretched  side  by  side,  transverse  to  the 
cochlea,  and  called  after  their  discoverer,  fibers  of  Corti.  On  this 
diaphnigm  terminate  the  auditory  nerves.  ^Mien  the  liquid  vibrates, 
the  fibers  vibrate  in  unison,  the  nerve  terminals  are  stimulated,  and 
thus  the  sensation  of  sound  is  produced.  These  fibers  of  Corti  are 
of  different  lengths  and  presumably  are  stretched  with  different 
tensions.  They  therefore  have  different  natural  rates  of  vibration 
and  a  sympathetic  resonance  for  different  notes.  The  whole  has 
been  called  a  harp  of  several  thousand  strings. 

Were  these  fibers  of  Corti  verj'  free  in  their  vibration,  each 
would  respond  to  and  would  respond  stronglj^  only  to  that  partic- 
ular note  with  whose  frequency  it  is  in  unison.  Because  of  the  fact 
that  they  are  in  a  liquid,  and  possibly  also  because  of  the  manner 


ORIGIN  OF  THE  MUSICAL  SCALE  109 

of  their  terminal  connections,  they  are  considerably  damped.  Be- 
cause of  this  their  response  is  both  less  in  amount  and  less  selective 
in  character.  In  fact,  under  these  conditions,  not  one,  but  many 
fibers  vibrate  in  n-sjjonse  to  a  single  pure  note.  A  considerable 
length  or  area  of  tlie  diaphragui  is  excited.  So  long  as  the  exciting 
sound  remains  pure  in  (iualit.\-.  constant  in  pitch,  and  constant  in 
intensity,  the  area  of  the  diaphragm  affected  and  the  amplitude  of 
its  vibration  remain  imchanged.  If,  however,  two  notes  are  sounded 
of  nearly  the  same  pitch,  the  areas  of  tiie  diaphragm  affected  by  the 
two  notes  overlap.  In  tiic  ()Vi'riapi)ing  regitm  the  vil)rati()n  is  violent 
when  the  two  notes  are  in  the  same  phase,  weak  when  they  are  in 
opposite  phase.  The  result  is  the  familiar  jihenomena  of  beats. 
Such  beats  when  slow  are  not  disagreeable  and  not  without  musical 
value.  If  the  difference  between  the  two  notes  is  incre;ised,  the 
beats  become  more  rapid  and  more  disagreeable.  To  this  violent 
disturbance,  to  the  starling  and  stopping  of  the  vibration  of  the 
fibers  of  Corti,  Ilclniholtz  ascribed  the  sense  of  roughness  which  we 
call  discord.  As  tlu'  notes  are  more  widely  separated  in  ])itch,  the 
overlai)ping  of  the  affected  areas  (liiiiiuislies.  Between  pure  notes 
the  sense  of  discord  disappears  willi  suliiciint.  separation  in  pitcli. 
When  the  two  vibrating  areas  exactly  match,  because  the  two  notes 
are  of  exactly  the  same  pitcli,  and  when  the  two  areas  do  not  in  the 
least  overlap,  because  of  a  sufficiently  wide  separation  in  pitch,  the 
result  according  to  Hehnholtz  is  harmony.  Partial  overlajiping  of 
the  affected  areas  produces  beats,  and  the  roughness  of  beats  is 
discord.  Such,  reduced  to  its  fewest  elements,  is  Hehnholtz'  expla- 
nation of  the  harmony  and  discord  of  tones  which  are  pure. 

J{ul  no  nuisical  tone  is  simjjle.  It  always  consists  of  a  combina- 
tion of  so-called  partial  tones  which  l)ear  to  eacli  other  a  more  or 
less  simple  relationship.  Of  these  partial  tones,  one  is  called  the 
fuudaniental, — .so-called  i)ecause  it  is  the  loudest  or  lowest  or, 
better  still,  becau.se  it  is  thai  to  which  the  oilier  partial  tones  bear 
the  simjilest  relation.  A  nmsical  tone,  therefore,  affects  not  one, 
bill.  Ilirougli  its  fundamental  and  ujjper  partial  toiieS,  several  areas 
of  the  diaphragm  in  the  cochlea.  Two  niusiral  tones,  each  with  its 
fiindanuntal  and  upper  parlials.  Ilu-refore.  affect  areius  of  the  dia- 
phragm which  overlap  each  other  in  a  more  or  less  complicated 


110  MELODY 

iiianncr,  (It'ix'ndinf;  dii  tlic  relative  frequencies  of  tlie  fundamentul 
tones  and  the  relationships  of  tlieir  upper  partials.  The  exact 
matching  of  the  arejis  affected  by  these  two  systems  of  partial  tones, 
or  the  entire  separation  of  the  affected  areas,  give  luirmony.  The 
overhii)i)ing  of  these  affected  areas,  if  great,  prochices  discord,  or.  if 
slight  in  amount,  modifications  and  color  of  harmony. 

In  the  great  majority  of  musical  tones  the  upper  partials  bear 
simple  relationships  to  the  fundamentals,  being  integral  multiples 
in  vibration  frequency.  Helmlioltz  showed  that  if  of  two  such 
tones  one  continued  to  sound  unchanged  in  pitch,  and  the  other 
starting  in  unison  was  gradually  raised  in  pitch,  the  resulting  dis- 
cord would  pass  through  maxima  and  minima,  and  that  the  minima 
would  locate  the  notes  of  the  pentatonic  scale.  The  intermediate 
notes  of  the  complete  modern  musical  scale  are  determined  by 
a  repetition  of  this  process  starting  from  the  notes  thus  deter- 
mined. 

If  to  this  is  added  a  similar  consideration  of  the  mutual  inter- 
ference of  the  combinational  tones  which  are  themselves  due  to 
the  interaction  of  the  partial  tones,  we  have  the  whole,  though  of 
course  in  the  briefest  outline,  of  Helmlioltz'  theory  of  the  harmony 
and  discord  of  simultaneously  sounding  musical  tones. 

Having  thus  in  Parts  I  and  II  developed  a  theory  for  the  har- 
mony and  discord  of  simultaneous  sounds,  and  having  developed 
a  theory  which  explains  the  modern  use  of  the  musical  scale  in 
chords  and  hannonic  music,  Helmlioltz  pointed  out,  in  Part  III, 
tliat  the  musical  scale  in  its  present  form  existed  before  the  inven- 
tion of  harmonic  music  and  before  the  use  of  chords. 

Music  may  be  divided  into  three  principal  periods :  — 

1.  "Homophonic  or  Unison  Music  of  the  ancients,"  including  the  music 

of  the  Christian  era  up  to  the  eleventh  century,  "  to  which  also 
belongs  the  existing  music  of  Oriental  and  Asiatic  nations." 

2.  "Polj-phonic  music  of  the  middle  ages,  with  several  parts,  but  with- 

out regard  to  any  independent  musical  significance  of  the  har- 
monies, extending  from  the  tenth  to  the  seventeenth  centurj'." 

3.  "Hannonic  or  modern   music  characterized   by   the   independent 

significance  attributed  to  the  harmonies  as  such." 


ORIGIN  OF  THE  ^^'SI^AL  SCALE  111 

Polyphonic  music  was  the  first  to  cull  for  the  production  of 
simultaneous  sounds,  and,  therefore,  for  the  hearing  or  the  experi- 
ence of  musical  harmony.  Homophonic  music,  tliat  which  alone 
existed  up  to  the  tenth  or  eleventh  century,  consisted  in  tiie  pro- 
gression of  single-part  melody.  Struck  by  this  fact,  Ilelmholtz 
recognized  the  necessity  of  seeking  another  explanation  for  tiie 
invention  and  the  use  of  a  scale  of  fixed  notes  in  the  music  of  this 
period.  To  borrow  his  own  words,  "scales  existed  long  before 
there  was  any  knowI(>dge  or  experience  of  hannony."  Again,  else- 
where, he  says  in  emphasizing  the  point:  "Tlie  indi\idual  parts  of 
melody  reach  the  ear  in  succession.  We  cannot  perceive  them  all 
at  once;  we  cannot  observe  backwards  and  forwards  at  pleasure." 
Between  sounils  [)roduced  and  heard  in  discrete  succession,  there 
can  be  neither  harmony  nor  discord,  there  cannot  be  beats,  or 
roughness  or  interruption  of  continuous  vibrations.  Regarding  the 
sounds  of  a  melody  as  not  merely  written  in  strict  and  non-over- 
lapping succession,  but  also  as  produced  and  heard  in  discrete  suc- 
cession, Hclmholtz  sought  another  b;usis  for  the  choice  of  the  notes 
to  constitute  a  scale  for  homophonic  music.  His  explanation  of 
this  invention  can  be  best  presented  l)y  a  lew  (juotations:  — 

Melody  has  to  esqjress  a  motion  in  siu-li  a  inamicr  that  the  hearer  may 
easily,  clearly,  and  certainly  appreciate  tlie  eliaracter  of  tliat  motion  hy 
iininediale  i)erce])ti()n.  This  is  only  possible  wiieii  the  steps  of  tiiis  motion, 
their  rapidity,  and  tiicir  amount,  are  also  exactly  measurable  by  immediate 
sensible  ]K'rcei)ti<)n.  Melodic  motion  is  ciiaiige  of  j)itch  in  time.  To  meas- 
ure it  perfectly,  the  lenfjlli  of  time  elapsed  and  llie  tlistanee  between  the 
pitches  must  be  measurable.  This  is  possible  for  immediate  audition  only 
on  condition  that  the  alterations  both  in  time  and  pitch  should  proceed  by 
regular  and  dclcrniiiiate  degrees. 

Again  Hclniiiollz  says:  — 

For  a  clear  and  sure  measurement  of  tlie  change  of  pitch  no  means  was 
left  but  progression  by  determinate  degrees.  This  scries  of  degrees  is  laid 
down  in  the  musical  scale.  When  the  wind  howls  and  its  pitch  rises  or  falls 
in  insensible  gradations  without  any  break,  we  have  nothing  to  measure 
the  variations  of  pitch,  nothing  by  which  we  can  compare  the  later  with  the 
earlier  sounds,  and  comprehend  the  extent  of  the  change.  The  whole  phe- 
nomenon i)r(>(hices  a  confused,  unpleasant  impression.  The  nnisical  scale 
is  as  it  were  the  divided  rod,  by  which  we  measure  progression  in  pitch,  as 
rhythm  measures  progression  in  time. 


Ibi  MKLODY 

I^ter  lie  says:  — 

Lot  us  begin  with  the  Octave,  in  which  the  relationship  to  the  funda- 
mental tone  is  most  remarkable.  I^t  any  melody  be  executed  on  any  in- 
strument which  has  a  good  musical  quality  of  tone,  such  as  a  human  voice; 
the  hearer  must  have  heard  not  only  the  primes  of  the  compound  tones,  but 
also  their  upf)er  octaves,  and.  less  strongly,  the  remaining  upper  partials. 
When,  then,  a  higher  voice  afterwards  executes  the  same  melody  an  Octave 
higher,  we  hear  again  a  part  of  what  we  heard  before,  namely  the  evenly 
iiiiml)ered  i)artial  tones  of  the  former  compound  tones,  and  at  the  same 
time  we  hear  nothing  that  we  had  not  jjreviously  heard. 

AVhat  is  true  of  the  Octave  is  true  in  a  less  degree  for  the  Twelfth. 
If  a  melody  is  repeated  in  the  Twelfth  we  again  hear  only  what  we  had 
already  heard,  but  the  repeated  part  of  what  we  heard  is  much  weaker, 
because  only  the  third,  sixth,  ninth,  etc.,  partial  tone  is  repeated,  whereas 
for  re])etition  in  the  Octave,  instead  of  the  third  partial,  the  much  stronger 
.second  and  weaker  fourth  partial  is  heard,  and  in  place  of  the  ninth,  the 
eighth  and  tenth  occur,  etc. 

For  the  repetition  on  the  Fifth,  only  a  part  of  the  new  sound  is  iden- 
tical with  a  part  of  what  had  been  heard,  but  it  is,  nevertheless,  the  most 
perfect  repetition  wliicl)  can  be  executed  at  a  smaller  interval  than  an 
Octave. 

^Vithout  carrying  these  quotations  further  they  will  sufRce  to 
illustrate  the  basis  which  Helmholtz  would  ascribe  to  homophonic 
music  and  early  melodic  composition.  On  this  explanation  the 
basis  of  melody  is  purely  that  of  rhythm  and  rhythm  based  on  a 
scale  of  intervals.  The  scale  of  intervals  in  turn  is  based  on  a 
recognition,  conscious  or  subconscious,  of  the  compound  character 
of  nnisical  tones,  and  of  the  existence  in  tones  of  different  pitch  of 
l>artials  of  the  same  pitch.  This  calls  for  a  degree  of  musical  in- 
sight and  discrimination  which  it  is  difficult  to  credit  to  a  primitive 
art.  It  is  in  reality  the  skill  of  the  highly  trained  musician,  of  a 
musician  trained  by  long  experience  with  sounds  which  are  rich 
and  accurate  in  quality.  This  power  of  analysis  goes  rather  with 
supreme  skill  than  with  the  early  gropings  of  an  art. 

MWr  liaving  developed  a  theory  of  harmony  and  discord  based 
on  elaborate  experimental  and  mathematical  investigations,  which 
was  remarkable  in  bringing  together  three  such  diverse  fields  as 
physics,  physiology,  and  aesthetics,  he  relegated  it  to  the  minor 
ajjplication  of  explaining  the  use  in  modern  music  of  an  already 


ORIGIN  OF  THE  MUSICAL  SCALE  113 

existing  and  highly  developed  musical  scale,  and  sought  an  expla- 
nation of  the  earlier  use  of  the  scale  in  melody  and  its  original  in- 
vention in  the  principle  which  is  very  far  from  possessing  either 
the  beauty  or  the  convincing  (juality  of  his  earlier  hypothesis.  He 
was  forced  to  this  by  a  i^riorily  of  melodic  or  homophonic  compo- 
sition. He  saw  in  melody  only  a  succession  of  notes,  no  two  exist- 
ing at  the  same  time,  and  therefore  incapable  of  producing  harmony 
or  discord  in  a  manner  such  as  he  had  been  considering. 

It  is  true  that  melody  is  written  as  a  pure  succession  of  discrete 
notes,  one  beginning  only  when  the  otlier  has  cetised.  It  is  true  also 
that  melody  is  so  sung  and  so  produced  on  a  homophonic  instru- 
ment, such  as  the  voice,  flute,  reeds,  or  one-stringed  instruments. 
This  is  peculiarly  true  of  the  voice,  and  it  is  with  the  voice  that 
one  naturally  associates  the  earliest  invention  of  the  .scale.  But 
while  it  is  true  that  the  earliest  song  must  have  consisted  of  tones 
produced  only  in  succession,  it  is  not  necessarily  true  tliat  such 
sounds  were  heard  as  isolated  notes.  A  sound  produced  in  a  space 
which  is  in  any  way  c-onfined  continues  until  it  is  diminished  by 
transmission  tlirou^Mi  ojx-nings  or  is  absorbed  by  the  retaining  walls, 
or  contained  iiiatcriai  to  such  a  point  tliat  it  is  past  llic  threshold 
of  audibility,  and  this  prolongation  of  audibility  of  sound  is  under 
many  conditions  a  factor  of  no  inc()nsi(leral)le  iiniiortance.  In  many 
rooms  of  ordinary  construction  the  prolongation  of  audibility 
amounts  to  two  or  three  seconds,  and  it  is  not  exceedingly  rare  that 
a  sound  of  moderate  initial  intensity  should  continue  audible  for 
eight,  nine,  or  ev'en  ten  seconds  after  the  source  has  ceiised.  As  a 
result  of  this,  single-part  nuisic  produced  as  successive  separate 
sounds  is,  nevertheless,  heard  as  overlapi)ing,  and  at  times  as  greatly 
overlaj)j)ing  tones.  Each  note  maj*  well  be  audible  with  appreciable 
intensit\-  not  incrcly  through  the  next.  Itut  through  several  suc- 
ceeding notes.  I  lulcr  such  conditions  we  iiave  every  opportunity, 
even  with  single-i)arl  nuisie,  for  llu-  production  of  all  the  |)lR'noiiiena 
of  harmony  and  discord  which  has  been  discussed  by  Helmholtz  in 
explanation  of  the  cliorilal  nse  of  llu-  iiiiisical  scale.  In  any  ordi- 
narily bare  and  uncari)eled  room,  one  may  sing  in  succession  a 
.series  of  notes  and  thru  hear  for  .some  time  afterward  their  full 
ehordal  etlVcl. 


lU  MELODY 

All  the  arpiimonts  that  Ilelmholtz  advanced  m  support  of  his 
iiypothi'sis.  that  the  nuisical  scale  was  devised  solely  from  con- 
siderations of  rliythm  and  founded  on  a  repetition  of  faint  upper 
partials,  hold  with  equal  force  in  the  explanation  here  proposed. 
The  identity  of  jiartial  tones  in  compound  tones  with  different 
fundamentals  is  one  of  the  conditions  of  harmony,  antl  the  scale 
devised  by  considerations  of  the  mutual  harmony  of  the  notes 
sounded  simultaneously,  would,  in  every  respect,  be  the  same  as 
that  of  a  scale  based  on  repeated  upper  partials.  In  the  one  case 
the  identity  of  upper  partials  is  an  act  of  memory,  in  the  other  it 
is  determined  by  the  harmony  of  sustained  tones.  All  the  argu- 
ments by  Helmholtz  based  on  historical  considerations  and  on 
racial  and  national  differences  are  equally  applicable  to  the  hy- 
pothesis of  sustained  tones.  In  fact,  they  take  on  an  additional 
significance,  for  we  may  now  view  all  these  differences  not  merely 
in  the  light  of  differences  in  racial  development  and  temperament, 
but  in  the  light  of  physical  environment.  Housed  or  unhoused, 
dwelling  in  reed  huts  or  in  tents,  in  houses  of  wood  or  of  stone,  in 
houses  and  temples  high  vaulted  or  low  roofed,  of  heavy  furnish- 
ing or  light,  in  these  conditions  we  may  look  for  the  factors  which 
determine  the  development  of  a  musical  scale  in  any  race,  which 
determine  the  rapidity  of  the  growth  of  the  scale,  its  richness,  and 
its  considerable  use  in  single-part  melody. 

The  duration  of  audibility  of  a  sound  depends  on  its  initial  in- 
tensity and  on  its  pitch,  to  a  small  degree  on  the  shape  of  the  con- 
fined space,  and  to  a  very  large  degree  on  the  volume  of  the  space 
and  on  the  material  of  which  the  walls  are  composed.  The  duration 
of  audiijility  is  a  logarithmic  function  of  the  initial  intensity,  and 
as  the  latter  is  practically  always  a  large  multiple  of  the  minimum 
audible  intensity,  this  feature  of  the  problem  may  be  neglected 
when  considering  it  broadly.  For  this  discussion  we  may  also  leave 
out  of  consideration  the  effect  of  shape  as  being  both  minor  and  too 
intricately  variable.  The  pitch  here  considered  will  be  the  middle 
of  the  musical  scale;  for  the  extremes  of  the  scale  the  figures  would 
be  very  different.  The  problem  then  may  be  reduced  to  two  factors, 
volume  and  material.  It  is  easy  to  dispose  of  the  problem  reduced 
to  these  two  elements. 


ORIGIN  OF  THE  MUSICAL  SCALE  115 

The  duration  of  audibilily  of  a  sound  is  directly  proportional  to 
the  volume  of  a  room  and  inversely  proportional  to  the  total  ab- 
sorbing power  of  the  walls  and  the  contained  material.  The  volume 
of  the  room,  the  shape  remaining  the  same,  is  proportional  to  the 
cul)e,  while  the  area  of  tlic  walls  is  proportional  to  the  square  of 
the  linear  dimensions.  The  duration  of  audibility,  proportional  to 
the  ratio  of  these  two,  is  proportional  to  the  first  power  of  the  linear 
dimension.  Other  things  being  equal,  the  duration  of  audibility, 
the  overlapping  of  successive  .sounds,  and,  therefore,  the  experience 
of  harmony  in  single-part  music  is  proportional  to  the  linear  di- 
mensions of  the  room,  be  it  dwelling  house  or  temple. 

Turning  to  the  question  of  material  the  followmg  figures  are 
suggestive:  Any  opening  into  the  outside  space,  provided  that 
outside  space  is  itself  unconfined,  may  be  regarded  as  being  totally 
absorbing.  The  absorbing  jiower  of  hard  pine  wood  sheathing 
of  one-half  inch  thickness  is  6.1  per  cent;  of  plaster  on  wood  lath, 
3.4  per  cent;  of  single-thickness  glass,  2.7  per  cent;  of  brick  in 
Portland  cement,  2.5  per  cent;  of  the  same  brick  painted  with  oil 
paint,  1.4  percent.  Wood  sheathing  is  nearly  double  any  of  the 
rest.  On  the  other  hand,  a  man  in  the  ordinary  clothing  of  today 
is  equal  in  liis  absorbing  power  to  nearly  48  per  cent  of  that  of  a 
square  meter  of  unobstructed  opening,  a  woman  is  54  per  cent,  and 
a  square  meter  of  audience  at  ordinary  seating  distance  is  nearly 
90  JHT  cent.  Of  significaiue  also  in  this  connection  is  the  fact  that 
Oriental  rugs  have  an  absorbing  power  of  nearly  29  per  cent,  and 
house  plants  of  11  percent. 

Of  course,  the  direct  a])i)licalion  of  these  figures  in  any  accurate 
calculation  of  the  conditions  of  life  among  different  races  or  at  dif- 
ferent jieriods  of  time  is  inijjossible,  but  they  indicate  in  no  uncer- 
tain manner  tiie  great  differences  acoustically  in  the  environment 
of  Asiatic  races,  of  aboriginal  r.ices  in  central  and  southern  Africa, 
of  the  Mediterranean  countries,  of  northern  Eurojje  at  different 
periods  of  time.  NVe  have  ex|)hiiiud  for  us  by  these  figures  why  the 
nnisical  scale  hiis  but  slowly  develojx'd  in  the  greater  part  of  Asia 
and  of  Africa.  .Vlniost  no  traveler  has  reported  a  nnisical  .scale, 
even  of  the  most  primitive  sort,  among  any  of  the  ])reviously  un- 
visiled  tribes  of  Africa.     This  fad  could  not  be  aseril)ed  to  racial 


11  (J  MELODY 

inapt ilw(K'.  If  im-lody  was,  as  Ilelnilioltz  suggested,  but  rhythm  in 
time  and  in  pitch,  the  musical  scale  should  have  been  developed  in 
Africa  if  anywhere.  These  races  were  given  to  the  most  rhythmical 
dancing,  and  the  rhj^hmical  beating  of  drums  and  tomtoms. 
Rhythm  in  time  they  certainly  had.  ^Moreover,  failure  to  develop 
a  musical  scale  could  not  be  ascribed  to  racial  inaptitude  to  feeling 
for  pitch.  Transported  to  America  and  brought  in  contact  with 
the  musical  scale,  the  negro  became  immediately  the  most  musical 
part  of  our  poi)ulation.  The  absence  of  a  highly  developed  scale  in 
Africa  nuist  then  be  ascribed  to  environment. 

Turning  to  Eiu"ope  we  find  the  musical  scale  most  rapidly  de- 
veloping among  the  stone-dwelling  people  along  the  shores  of  the 
Mediterranean.  The  development  of  the  scale  and  its  increased 
use  kept  pace  with  the  increased  size  of  the  dwellings  and  temples. 
It  showed  above  all  in  their  religious  worship,  as  their  temples  and 
churches  reached  cathedral  size.  The  reverberation  which  accom- 
panied the  lofty  and  magnificent  architecture  increased  until  even 
the  spoken  service  became  intoned  in  the  Gregorian  chant.  It  is 
not  going  beyond  the  bounds  of  reason  to  say  that  in  those  churches 
in  Europe  which  are  housed  in  magnificent  cathedrals,  the  Catholic, 
the  Lutheran,  and  Protestant  Episcopal,  the  form  of  worship  is  in 
part  determined  by  their  acoustical  conditions. 

This  presents  a  tempting  opportunity  to  enlarge  on  the  fact 
that  the  alleged  earliest  evidence  of  a  musical  scale,  a  supposed 
flute,  belonged  to  the  cave  dwellers  of  Europe.  This  and  the  im- 
pulse to  sing  in  an  empty  room,  and  the  ease  with  which  even  the 
unmusical  can  keep  the  key  in  simple  airs  under  such  conditions, 
are  significant  facts,  but  gain  nothing  by  amplification.  The  same 
may  be  said  of  the  fact  that  since  music  has  been  wTitten  for  more 
crowded  auditoriums  and  with  harmonic  accompaniment  melody 
has  become  of  less  harmonious  sequence.  These  and  many  other 
instances  of  the  effect  of  reverberation  come  to  mind. 

In  conclusion,  it  may  not  be  out  of  place  to  repeat  the  thesis 
that  melody  may  be  regarded  not  only  as  rhythm  in  time  and 
rhythm  in  pitch,  but  also  as  harmony  in  sustained  tones,  and  that 
we  may  see  in  the  history  of  music,  certainly  in  its  early  beginnings, 
but  possibly  also  in  its  subsequent  development,  not  only  genius 
and  invention,  but  also  the  effect  of  physical  environment. 


ARCHITECTURAL  ACOUSTICS^ 
EFFECTS  OF  AIR  CURRENTS  AND  OF  TEMPERATIRE 

V/RDiXAUiLY  there  is  not  :i  close  connection  between  the  flow  of 
air  in  a  room  and  its  acoustical  properties,  although  it  has  been  fre- 
quently suggested  that  thus  the  sound  may  be  carried  effectively 
to  different  parts.  On  the  other  hand,  while  the  motion  of  the  air 
is  of  minor  importance,  the  distribution  of  temperature  is  of  more 
importance,  and  it  is  on  reliable  record  that  serious  acoustical  diffi- 
culty has  arisen  from  abrupt  differences  of  temperature  in  an  audi- 
torium. Finally,  transmission  of  disturbing  noises  through  the 
ventilation  ducts,  jjcrhaps  theoretically  a  side  issue,  is  practically 
a  legitimate  and  necessary  jiart  of  the  subject.  The  discussion  will 
be  under  these  three  heads. 

The  first  of  the  above  three  topics,  the  possible  eflFect  of  the  mo- 
tion of  the  air  on  the  acoustical  property-  of  a  room,  is  the  immediate 
subject . 

Ventilation 

It  was  suggested  during  the  jilanning  of  the  Boston  Symphony 
Hall  that  its  acoustical  properties  would  be  greatly  benefited  by 
introducing  the  air  for  ventilation  at  the  front  and  exhausting  at 
the  back,  thus  carrying  the  sound  by  the  motion  of  the  air  the  length 
of  the  room.  The  same  suggestion  has  been  made  to  the  writer  by 
others  in  regard  to  other  buildings,  but  this  case  will  serve  ius  suffi- 
cient example.  The  suggestion  was  unoflicial  and  the  gentleman 
proi)osing  it  accompaniicl  it  by  a  section  of  a  very  different  hall  from 
the  hall  designed  by  Mr.  McKim,  but  as  this  section  was  only  a 
sketch  and  without  dimensions  the  following  calculation  will  be 
made  as  if  the  idea  were  to  be  applied  to  the  present  hall.  It  will 
be  shown  that  the  result  thus  to  be  secured,  while  in   the   right 

'  Engineering  HcconI,  .Juih',  lOUt. 
IIT 


lis  ARCHITECTURAL  ACOUSTICS 

direction,  is  of  a  magnitude  too  small  to  be  appreciable.  To  make 
this  the  more  decisive  we  shall  assume  throughout  the  argument 
the  most  favorable  conditions  possible. 

If  a  sound  is  produced  in  still  air  in  open  space  it  spreads  in  a 
sjjherical  wave  diminishinf^  in  intensity  as  it  covers  a  greater  area. 
The  area  of  a  sphere  being  i)roportioned  to  the  square  of  the  radius, 
we  arrive  at  the  common  law  that  the  intensity  of  sound  in  still  air 
is  inversely  proportional  to  the  square  of  the  distance  from  the 
source.  If  in  a  steady  wind  the  air  is  moving  imiformly  at  all  alti- 
tudes, the  sound  still  spreads  spherically,  but  with  a  moving  center, 


Fig.  1 

the  whole  sphere  being  carried  along.  If  the  air  is  moving  toward 
the  observer,  the  sound  reaches  him  in  less  time  than  it  otherwise 
would,  therefore  spread  over  a  less  spherical  surface  and  louder. 
If,  on  the  other  hand,  the  observer  is  to  windward,  the  sound  has 
had  to  come  against  the  wind,  has  taken  a  longer  time  to  reach  him, 
is  distributed  over  a  greater  surface,  and  is  less  loud. 

The  three  cases  are  represented  in  the  accompanj^ing  diagram. 
The  stationary  source  of  sound  being  at  S,  a  is  the  wave  in  still  air 
arriving  at  both  observers  at  the  same  time  and  with  the  same  in- 
tensity. If  the  air  is  moving  to  the  left,  the  center  of  the  wave  will 
be  shifted  by  an  amount  d  to  the  left  while  the  wave  has  spread  to 
Oi.  On  arrival  it  will  have  the  size  h,  less  than  a,  and  will  be  louder. 
On  tlie  other  hand,  while  the  wave  is  reaching  02,  the  observer  to 
windward,  the  center  will  have  been  shifted  to  the  left  by  an  even 
greater  amount  ^2-  In  this  case  the  size  of  tlie  wave  will  be  c,  larger 
than  a,  and  the  sound  will  be  less.  The  loudness  of  the  sound  in  the 
three  cases  is  inversely  as  the  three  surfaces  a,  b,  and  c.    If  the  dis- 


b 


EFFECTS  OF  AIR  CITRREXTS  119 

tance  of  tlie  observer  Iroin  S  is  denoti-d  by  r,  the  loudness  of  the 
sound  in  the  three  cases  will  be  as 

1         1  ■        1 

The  above  result  iiuiy  lie  expressed  in  the  following  nioic  simple 
and  practical  form.  II',  in  the  diagram,  a  is  lli<-  wave  in  still  air,  it 
corresponding  position  wiieii  of  the  same  size  and,  therefore,  of  the 
same  intensity  in  moving  air  will  he  a',  the  movement  of  the  air 
having  been  sufficient  to  carry  the  wave  a  distance  d  while  it  has 
expanded  witii  the  velocity  of  sound  to  a  sphere  of  radius  r.  The 
distance  d  and  the  radius  r  are  to  each  other  as  the  velocity  of  wind 
and  the  velocity  of  sound.  If  thi>  observers  o,  and  Oo  move,  the  one 
away  from  the  source  and  the  other  toward  it,  by  a  distance  d,  the 
sound  will  be  of  the  same  intensity  to  both  as  in  their  first  positions 
in  still  air. 

In  order  to  make  ajjplication  of  this  to  the  particular  problem 
in  hand,  we  shall  assume  a  normal  air  su])ply  to  the  room  for  ven- 
tilation i)urposes  of  one-sevciitictli  of  a  culjic  meter  per  person  per 
second.  This,  if  intiodnccd  all  at  one  end  and  exhausted  all  at  the 
other,  in  a  room  17.9  meters  high,  'i'i.H  meters  broad,  and  seating 
about  '■2()()()  persons,  would  produce  a  velocity  of  the  air  of  0.09 
meters  per  second,  assuming  the  velocity  to  be  the  same  at  every 
point  of  a  transverse  .section.  Leaving  out  of  account  the  ques- 
tionable merits  of  this  arrangement  from  the  ventilation  standpoint, 
its  acoustical  value  can  be  calculated  readily. 

The  velocity  of  sound  under  normal  conditions  being  about 
340  meters  per  second,  the  time  required  to  traverse  a  hall  40  meters 
long  is  only  about  one-ninth  of  a  second.  In  tiiis  short  inler\al  of 
time  the  motion  of  the  air  in  the  room,  due  to  the  ventilation,  would 
be  sufficient  to  advance  the  sound-wave  only  0.01  meters,  or  one  cen- 
timeter. It  would  thus  arrive  at  the  liaek  of  the  room  ius  a  sphere 
with  its  center  one  centimeter  nearer  than  t  he  source.  That  is  to saj', 
the  beneficial  effect  of  this  proposed  system  of  ventilation,  greatest 
for  the  auditor  on  the  rear  seal,  would  to  him  be  equivalent  at  the 
very  maxinuun  to  bringing  the  stage  into  the  room  one  centimeter 
further,  or  it  would  be  equivalent  to  bringing  the  auditor  on  the 


Ui)  ARCHITKCrrRAL  ACOUSTICS 

rear  scat  forward  ono  centimeter.  This  distance  is  so  sli^lit  tiiat 
without  niovinf,'  in  Ids  seat,  in  fact,  without  moving  his  shoulders, 
a  slipiit  inclination  of  the  liead  would  accomplish  an  equivalent 
gain.  Thvis,  while  the  effect  is  in  the  right  direction,  it  is  of  entirely 
iMii)ercei)til»le  magnitude.  If  we  take  into  account  the  sound  re- 
flected from  walls  and  ceiling,  the  gain  is  even  less. 

Hut  the  suggestion  which  is  the  text  of  the  present  paper  was 
not  made  by  one,  but  by  several  gentlemen,  and  is  based  on  the 
well-recognized  fact  that  one  can  hear  better,  often  very  much 
better,  with  the  wind  than  against  it,  and  better  than  in  still  air. 
Therefore,  the  suggestion  is  not  groundless  and  cannot  be  disposed 
of  tlius  summarily,  certainly  not  witliout  submitting  to  the  same 
calculation  the  out-of-door  experience  that  gave  rise  to  the  thought. 

In  llu'  nomenclature  of  the  United  States  Weather  IJureau  a 
wind  of  from  "1  to  5  miles  an  hour  is  called  light,  6  to  14  miles 
fresh,  15  to  24  miles  brisk,  25  to  37  miles  high,  and  a  wind  of  from 
40  to  59  miles  is  called  a  gale."  Taking  the  case  of  a  "high  wind" 
as  a  liberal  example,  its  average  velocity  is  about  14  meters  per 
second,  or  about  one  twenty-hfth  the  velocity  of  sound.  In  such 
a  wind  the  sound  1000  meters  to  leeward  would  be  louder  than  in 
still  ;iir  only  by  an  amount  which  would  be  equivalent  to  an  ap- 
proach of  40  meters,  or  8  per  cent.  Similarly,  to  windward  the  sound 
would  b(>  less  loud  by  an  amount  equivalent  to  increasing  the  dis- 
tance from  1000  to  1040  meters.  This  is  not  at  all  conniiensurate 
with  general  experience.  The  difference  in  audibility,  everyone  w  ill 
agree,  is  generally  greater  and  very  much  greater  than  this.  The 
discre])ancy,  however,  can  l^e  explained.  The  discrepancy  is  not 
between  observation  and  theory,  but  between  observation  and  a 
very  incomplete  analysis  of  the  conditions  in  the  out-of-door  ex- 
perience. Thus,  the  ordinary  view  is  that  one  is  merely  hearing 
with  or  against  the  wind  and  this  wand  is  thought  of  as  steady  and 
uniform.  As  a  matter  of  fact,  the  wind  is  rarely  steady,  and  partic- 
ularly is  it  of  different  intensity  at  different  altitudes.  Fortunately, 
the  out-of-door  phenomenon,  which  in  reality  is  very  complex,  has 
been  carefully  studied  in  connection  with  fog  signals. 

The  first  adequate  ex-planation  of  the  variation  in  loudness  of  a 
sound  with  and  against  the  wind  was  by  the  late  Sir  George  G. 


EFFECTS  OF  AIR  CT'RREXTS  121 

Stokes  in  an  article  "On  the  Eft'ect  of  Wind  on  the  Inten.sit\-  of 
Sound,"  in  the  Report  of  the  Brititih  Association  for  the  Advancement 
of  Science  for  1857.    The  complete  paper  is  as  follows: 

The  reinarkiihk'  (liinimilioii  in  tlic  intensity  of  sound,  wliicli  is  produced 
when  a  slroiij;  wind  Mows  in  a  direction  from  tlie  ol)server  toward  the 
source  of  sound,  is  familiar  to  everyhody,  hut  has  not  liitlierto  heen  ex- 
plained, so  far  as  I  lie  Miidmr  is  aware.  At  first  sight  we  might  he  disposed 
to  attriltute  it  merely  to  t  lie  increase  in  the  radius  of  the  sound-wave  wliieh 
reaches  tiie  ohserver.  The  whole  mass  of  air  heini,'  su])])osed  to  he  carried 
uniformly  along,  the  time  which  the  sound  would  take  to  reach  the  ol>- 
.server,  and  conse(|uently  the  radius  of  the  sound-wa\-e  would  he  increased 
hy  the  wind  in  the  ratio  of  the  \clocity  of  souiul  to  the  smn  of  the  velocities 
of  sound  and  of  the  wind,  and  the  intensity  would  he  diminished  in  the 
inverse  du])licate  ratio.  Hut  the  t  H'ect  is  nuieh  too  great  to  he  attril>utal)le 
to  this  cause.  It  woulii  he  a  strong  wind  whose  velocity  was  a  twenty- 
fourth  part  of  that  of  soun<l;  yet  e\eii  in  this  case  the  intensity  wnuM  l)e 
diminished  hy  only  ahout  a  twelfth  ])art. 

The  first  \-olume  of  the  Aiiiialr.s  tie  Chimie  (1816)  contains  a  |)aper 
hy  M.  Delaroclic,  giving  the  ri-sults  of  some  experiments  nuide  on  this 
suhject.  It  appeared  from  the  experiments,  first,  that  at  small  distances 
the  wind  has  hardly  any  |)erceptil)le  cit'cct,  the  sound  heing  propagated 
almost  equally  well  in  .-i  (lirectidn  conlrary  to  llic  wind  .ind  in  (he  direction 
of  the  wind;  second,  that  the  disi)arity  hetwcen  the  intensity  |)ro|)agateti 
in  these  two  directions  I)e<'omes  proportionally  greater  and  greater  as  the 
distance  increases;  third,  that  soun<l  is  jirojiagated  rather  liettcr  in  a  direc- 
tion ])er])endicular  to  the  wind  than  even  in  the  direction  of  the  wind.  The 
ex])lanation  offered  hy  the  author  of  the  present  conununication  is  as 
follows : 

If  we  imagine  the  wlioh-  mass  of  air  in  the  neighhorhood  of  the  source  of 
disturhancc  di\ided  into  horizontal  strata,  these  strata  do  not  move  with 
the  .same  \cl(icily.  Tlu-  lower  strata  arc  retarded  hy  friction  against  the 
earth  and  hy  the  various  ohstacles  they  meet  with;  the  upper  hy  fri<-tion 
against  the  iow<-r,  and  so  on.  Hence,  the  velocity  increas<'s  from  the 
ground  ui)ward,  conformalily  with  oh.servation.  This  increa.se  of  velocity 
disturhs  the  spherical  form  of  the  sound-wave,  tending  to  make  it  M>me- 
wliat  of  the  form  of  an  ellipsoid,  the  se<-tion  of  which  hy  a  \'ertii-al  diametral 
])lanc  parallel  to  thi'  direction  of  the  winil  is  an  ellipse  meeting  the  ground 
at  an  ohtuse  angle  on  the  side  towards  which  th<-  wiriil  is  hlowing,  and  an 
acute  angle  on  the  opposite  side. 

Now,  sound  tends  to  projiagate  it.self  in  a  direction  iHTpendiiular  to  tin- 
sound-wave;  and  if  a  |)orlion  of  the  wave  is  intercepted  l>y  an  oiotai-je  of 
larger  size  the  .space  Iwhind  is  left  in  a  .sort  of  .snund-shadow,  and  the  only 


li^i  ARCHITECTITIAL  ACOUSTICS 

sound  tluTc  lit-aril  is  wliat  tiiverges  from  the  {general  wave  after  i)assin<r 
till'  olislaclo.  Uriice.  near  tlio  oarlli.  in  a  dirfctioii  contrary  to  the  wind. 
the  soiiiul  continually  tends  to  I)c  i)ropaf,'ated  ui)\vards,  and  consequently 
there  is  a  eontiiuial  ten<lenoy  for  an  ol)server  in  tliat  direction  to  be  loft  in 
a  sort  of  sound-slia<lo\v.  Hence,  at  a  sufKcient  distance,  the  sound  ought 
to  he  \ery  much  enfeebled;  but  near  the  source  of  disturbance  this  cause 
has  not  yet  had  time  to  operate,  and,  therefore,  the  wind  produces  no 
sensil)le  effect,  exce|)t  wiiat  arises  from  the  augmentation  in  tlie  radius  of 
the  .sound-wave,  and  this  is  too  small  to  be  perceptible. 

In  the  contrary  direction,  that  is,  in  the  direction  towards  which  the 
wind  is  blowing,  the  sound  tends  to  propagate  itself  downwards,  and  to  be 
reflected  frotn  the  surface  of  the  earth;  and  both  the  direct  and  reflected 
waves  contribute  to  the  effect  perceived.  The  two  waves  assist  each  other 
so  nmch  the  better,  as  the  angle  between  them  is  less,  and  this  angle  van- 
ishes in  a  direction  perpendicular  to  the  wind.  Hence,  in  the  latter  direction 
the  .sound  ought  to  be  proj)agatctl  a  little  better  than  even  in  the  direction 
of  the  wind,  which  agrees  with  the  ex]jerinients  of  M.  Delaroche.  Thus, 
the  effect  is  referred  to  two  known  causes, —  the  increased  velocity  of  the 
air  in  ascending,  and  the  ditt'ractioTi  of  sound. 

As  a  matter  of  fact,  the  phenomenon  is  much  more  complicated 
when  one  takes  into  consideration  the  fact  that  a  wind  is  ahnost 
always  of  very  irregular  intensities  at  different  altitudes.  The 
phenomenon,  in  its  most  complicated  form,  has  been  investigated 
in  connection  with  the  subject  of  fog  signals  by  Professor  Osborn 
Reynolds  and  Professor  Joseph  Henry,  but  with  this  we  are  not  at 
l)resent  concerned,  for  the  above  discussion  by  Professor  Stokes  is 
entirely  sufficient  for  the  problem  in  hand. 

The  essence  of  the  above  explanation  is,  therefore,  this,  that  the 
great  difference  in  loudness  of  sound  with  and  against  the  wind  is 
not  due  to  the  fact  that  the  sound  has  been  simply  carried  forward 
or  opposed  by  the  wind,  but  rather  to  the  fact  that  its  direction  has 
been  changed  and  its  wave  front  distorted.  The  application  of  this 
consideration  in  the  present  architectural  problem  leads  to  the  con- 
clusion that  the  greatest  benefit  will  come  not  from  an  attempt  to 
carry  the  sound  by  the  ventilating  movement  of  the  air,  but  by 
using  the  motion  of  the  air  to  incline  the  wave  front  forward  and 
thus  direct  the  sound  down  upon  the  audience. 

This  can  be  done  in  either  one  of  two  ways,  by  causing  the  air 
to  flow  through  the  room  from  front  to  back,  more  strongly  at  the 


EFFECTS  OF  AIR  (T'RREXTS  123 

ceiling  than  at  the  floor,  or  by  causing  the  air  to  flow  from  tlie  back 
to  the  front,  more  strongly  at  the  floor  than  at  the  ceiling.  The  one 
process  carrying  the  upper  part  of  the  wave  forward,  the  other  re- 
tarding the  lower  part  of  I  he  wave,  will  tiji  the  wave  in  the  same 
way  and  by  an  equal  amount. 

Again,  taking  an  extreme  ca.se,  the  u.s.Munptioii  will  be  made  that 
the  motion  of  the  air  is  such  that  it  is  not  moving  at  or  near  the  floor, 
that  it  is  moving  with  its  maximum  \fl()(it,\-  at  the  ceiling,  ami  lliat 
the  increase  in  velocity  is  gradual  from  floor  to  ceiling.  Keeping 
the  same  amount  of  air  moving  as  in  the  preceding  calculation,  the 
velocity  of  the  air  under  this  arrangement  would  be  twice  a.s  great 
as  the  average  velocity  at  the  ceiling;  in  tiie  preceding  case  the 
wave  was  advanced  one  centimeter  by  the  motion  of  the  air  while 
traveling  the  whole  length  of  the  hall.  In  this  case,  obviously,  the 
upper  part  of  the  wave  would  be  carried  twice  as  far,  two  centime- 
ters, and  the  lower  part  not  advanced  at  all.  This  would,  therefore, 
measure  the  total  forward  tip  of  the  wave. 

Fortunately,  the  acoustical  value  of  this  can  be  exjiressed  in  a 
very  simple  and  practical  manner.  An  inclination  of  the  sound- 
wave is  ecjuivalent  acoustically  to  an  eiiual  angular  inclination  of 
the  floor  in  the  opposite  direction.  The  height  of  the  hail  being 
17.9  meters,  the  inclination  forward  of  the  sound-wave  would  be 
2  in  1790.  The  length  of  the  hall  being  40  meters,  an  equal  incli- 
nation, and  thus  an  equal  acoustical  efl'eet  woulil  be  produced  by 
raising  the  rear  of  the  floor  about  5  centimeters.  This  considers 
only  the  soimd  which  has  come  directly  from  the  stage.  It  is  ol>- 
vious  that  if  the  reflection  of  the  sound  from  the  ceiling  and  the  side 
walls  is  taken  into  account,  the  gain  is  even  less. 

It,  therefore,  ai)i)ears  that,  using  llie  motion  of  I  lie  air  in  the 
most  advantageous  wa\'  jjossiiile,  tlic  rouiliiig  iniprovemeul  in  tin- 
acoustical  i)roperty  of  the  hall  is  of  an  amount  absoluti-ly  negligible. 
A  negative  result  of  this  sort  is  jxThaps  not  so  interesting  as  if  a 
|)ositive  advaiitiige  has  i)een  shown;  but  the  problem  of  proiH-rly 
heating  and  ventilating  a  room  is  suflieieiilly  dillieult  in  itself,  and 
the  above  considerations  are  worth  whiK-  if  only  Id  free  it  from  this 
additional  coinpliealion. 


124  AIU'IHTKCTrHAl>  ACOUSTICS 

Temperature 

The  offecl  of  raising  tlu-  Uinperature  of  a  room,  involving  as  it 
does  the  contained  air  and  all  the  reflecting  walls  and  objects,  is 
twofold.  It  is  not  (lidicult  to  show  that,  whether  we  consider  the 
rise  in  teni])eralurc  of  I  lie  air  or  the  rise  in  temperature  of  the  walls 
and  other  reflecting  surfaces,  the  effect  of  a  change  of  temperature 
between  the  limits  which  an  audience  can  tolerate  is  negligible, 
provided  the  rise  in  temperature  is  uniform  throughout  the  room. 

The  effect  of  uniformly  raising  the  temperature  of  the  air  is  to 
increase  the  velocity  of  propagation  of  sound  in  all  directions.  It 
is,  therefore,  essentially  unlike  the  effect  produced  by  motion  of 
the  air.  In  the  case  of  a  uniform  motion  of  the  air,  the  sound  spreads 
spherically  but  with  unchanged  velocity,  moving  its  center  in  the 
direction  and  with  the  velocity  of  the  wind.  Thus,  when  blown 
toward  tlie  observer,  it  reaches  him  as  if  coming  from  a  nearer 
source.  Blown  away  from  the  observer,  it  arrives  as  from  a  more 
distant  source.  An  increasing  temperature  of  the  air  increases  the 
velocity,  but  does  not  shift  the  center.  The  sound  reaches  the  ob- 
server coming  from  a  source  at  an  unchanged  distance.  A  rise  in 
temperature,  therefore,  provided  it  be  uniform,  neither  increases 
nor  decreases  the  apparent  intensity  of  the  sound.  The  intensity 
at  all  points  remains  wholly  unaltered. 

TIic  above  is  on  the  assumption  that  the  temperature  of  the  air 
at  all  points  is  the  same.  If  the  temperature  of  the  air  is  irregular, 
the  effect  of  such  irregularity  may  be  pronounced;  for  example,  let 
us  assunu'  a  room  in  which  the  temperature  of  the  air  at  the  upper 
levels  is  greater  than  at  lower  levels.  In  order  to  make  the  case  as 
simple  as  possible,  let  us  assume  that  the  temperature  increases 
uniformly  from  the  floor  to  the  ceiling.  To  make  the  case  concrete, 
let  us  assume  that  the  hall  is  the  same  as  that  described  above, 
practically  rectangular,  40  X  22.8  X  17.9  meters.  The  velocity  of 
the  soimd  at  the  ceiling,  the  air  being  uniform,  is  greater  than  it  is 
at  the  floor.  In  traversing  the  room  the  sound-wave  will  thus  be 
tipped  forward.  The  effect  is  practically  equivalent  as  before  to  an 
increased  pitch  of  the  floor  or  to  an  increased  elevation  of  the  plat- 
form.   Without  going  into  the  details  of  this  very  obvious  calcula- 


EFFECTS  OF  AIR  (  lUUEXTS  1^25 

tion,  it  is  sufficient  to  siiy  that  in  IIr-  case  of  tlie  hall  here  taken  as 
an  example,  a  difference  of  temperature  top  and  Ijottom  of  10°  C. 
would  be  equivalent  to  an  increase  in  pitch  of  the  floor  sufficient  to 
produce  an  increased  elevation  of  the  very  back  of  10  centimeters. 
A  difference  in  temperature  of  10°  ('.  is  not  excessive,  and  it  is  obvi- 
ous that  this  has  a  greater  effect  than  has  that  of  the  motion  of  the 
air. 

In  the  above  discussion  of  the  effects  of  motion  and  of  tempera- 
ture on  the  acoustical  ciuality  of  a  room,  it  has  be(>n  assumed  that 
we  are  dealing  solely  with  the  sound  which  has  come  directly  from 
the  platform.  The  argument  holds  to  a  less  degree  for  the  sound 
reflected  from  the  ceiling  and  lioni  the  walls.  The  above  estimates, 
therefore,  are  outside  estimates.  The  effect  is  on  the  whole  cer- 
tainly less.  It  is  safe  to  say  that  the  total  attainal)le  result  is  not 
worth  the  effort  that  would  be  involved  in  altering  the  architectural 
features  or  in  comjjromising  the  engineering  ])iaiis. 

But,  while  uniforui  variatinn  in  liie  motion  or  in  the  temperature 
of  the  air  in  llie  room  .ire  on  the  whole  negligible  factors  in  its  acous- 
tical character,  this  is  by  no  nH:in>  true  of  irregularities  in  the 
temperature  of  the  air,  such  as  would  !»•  piniluced  iiy  a  colunin  <il 
warm  air  rising  from  a  floor  inlet.  That  this  is  a  ])ractical  point  is 
shown  by  the  testimony  of  Dr.  David  B.  Keid  beiore  the  Committee 
of  the  Houses  of  rarliament  ])ublislud  in  its  Report  of  lS;i.5.  This 
conuuittee  was  appointed  to  look  into  the  nuitter  of  the  heating, 
ventilation  and  acoustics  of  the  lious<s  which  were  being  designed 
to  replace  those  burned  in  IH'.Vi.  Of  the  gentlemen  called  before 
the  committee.  Dr.  Reid  gave  by  far  |1h>  b(>st  testimony,  i):irt  of 
which  was  as  follows. 

Speaking  of  the  hall  trnipoiMril.N  (i((U|)ic(l  by  I  lie  House  t)f 
Commons,  he  s:ii(l:  "WiiotluT  M>une  of  inlnruiilion  wliirli  might 
be  gmirded  against  is  tin-  great  ImhIv  dl'  air  which  1  prounic  arises 
wheiievt-r  the  heating  ai)i)aralu.s  i>  in  action  below.  In  dillVrenl 
buildings  I  have  li;id  (iceasion  to  renuirk  that  whenever  lln'  alnios- 
|)here  was  ])reserved  in  a  >tale  (if  unity  as  much  a>  possible.  et|Ual 
in  every  respect,  the  sound  was  uu)st  distinctly  audii>le:  it  occurred 
to  me  that  when  the  current  of  hot  air  rises  from  tin-  large  ap- 
paratus in  the  middle  of  the  House  of  Commons  it  would  very  likely 


l^e  AliCTUTECTURAL  ACOT'STICS 

iiilcrftTi'  with  the  conimunication  of  sound.  On  inquiry,  one  of  the 
gentlemen  now  i)resent  lohl  nie  lie  hud  frequently  observed  it  was 
impossible  to  hear  individuals  who  were  on  the  opposite  side  of  this 
current,  although  those  at  a  distance  were  heard  distinctly  where 
the  current  did  not  intervene."  Elsewhere  Dr.  Reid  said:  "A  cur- 
rent of  hot  air,  rising  in  a  broad  sheet  along  the  center  of  the  House, 
reflected  the  sountl  passing  from  side  to  side  and  rendered  the  in- 
tonation indistinct.  One  of  the  members  of  the  committee,  when  I 
exi)lained  this  circumstance,  stated  that  he  had  often  noticed  that 
he  could  not  hear  a  member  opposite  him  distinctly  at  particular 
times  unless  he  shifted  his  seat  along  the  bench,  and  on  examining 
the  place  referred  to,  it  was  found  that  he  had  moved  to  a  position 
where  the  hot  air  current  no  longer  passed  between  him  and  the 
member  speaking." 

A  more  recent  instance  of  this  sort  of  difficulty  was  mentioned 
to  the  writer  by  ^Ir.  W.  L.  B.  Jenney,  of  Chicago,  as  occurring  in 
his  practice,  and  later  was  described  in  detail  in  a  letter  from  which 
the  following  is  quoted : 

The  hiiildinf;  I  referred  to  in  my  conversation  was  a  court  house  at 
IxK-kjiort.  No  plans  exist  as  far  as  I  am  aware.  Note  the  sketch  I  made 
from  remembrance. 

Note  the  passage  across  the  room  witli  stove  in  center.  As  the  courts 
were  held  only  during  winter  there  was  invariably  a  fire  in  that  stove. 
When  I  examined  the  room  the  attendant  tliat  was  with  me  informed  me 
that  the  remarks  made  by  the  judge,  la\\yers  and  witness  could  not  be 
heard  In'  the  audience  on  the  opposite  side  of  the  passageway  containing 
the  stove. 

At  that  time,  the  court  room  not  l)eing  occupied,  there  was  no  fire  in 
the  stove  and  the  doors  were  closed.  I  experimented;  put  the  attendant 
in  the  judge's  stand  and  took  position  at  "A.".  I  could  hear  perfectly  well. 
I  spoke  to  liim  and  he  replied,  "AMiy,  I  can  hear  you  perfectly  well."  I 
reached  tiiis  conclusion.  Tliat  the  heated  air  from  the  stove  and  the  air 
supplied  by  the  doors  that  were  constantly  fanning  at  each  end  of  the 
passageway  prodviced  a  stratum  of  air  of  different  density  from  that  of 
the  other  parts  of  the  room,  wliich  acted  like  a  curtain  hanging  between 
the  speakers  and  the  hearers.  I  made  my  report  verbally  to  the  committee 
that  I  left  below  and  brought  them  with  me  to  the  room.  The  experiments 
were  renewed  and  they  accepted  my  theory.  I  recommended  that  the 
stove  be  moved  and  that  the  warm  air  should  be  let  into  the  room  from 
steam  coils  below  at  the  the  end  "A"  and  taken  out  by  exhaust  ventilators 


EFFECTS  OF  AIR  (  TTIREXTS  127 

at  the  end  "B."  This  was  done,  and  I  was  informed  hy  the  chairman  of 
the  comniittee  that  the  result  was  very  satisfactory.  Tlie  other  conditions 
of  the  room  were  quite  usual,  —  plasterinj;  on  wooden  lath,  wooden  floors, 
reasonable  height  of  ceiling. 

The  above  incidents  seem  to  demonstrate  fairly  clearly  thai 
under  certain  circumstances  abrupt  irregularities  in  temperature 
may  result  in  marked  and,  in  general,  unfavorable  acoustical  effects. 
The  explanation  of  these  effects  in  both  cases  is  somewhat  a,s  follows: 

Whenever  sound  passes  from  one  medium  to  another  of  dili'erent 
density,  or  elasticity,  a  portion  of  the  sound  is  reflected.  The  sound 
which  enters  the  second  medium  is  refracted.  The  effects  observed 
above  were  due  to  these  two  phenomena,  acting  jointly. 

The  first  of  the  two  cases  was  under  simpler  conditions,  and  is, 
therefore,  the  easier  to  discuss.  Essentiallj-,  it  consisted  of  a  large 
room  with  speaker  and  auditor  facing  each  other  at  a  comparatively 
short  distance  apart,  but  with  a  cylindrical  column  of  hot  air  rising 
from  a  register  immediately  between.  The  voice  of  the  speaker, 
striking  this  column  of  air,  lost  a  part  by  rcfh'clion;  a  i)art  of  the 
sound  passed  on,  entered  the  coluinii  of  warm  air,  and  came  to  the 
second  surface,  where  a  part  was  again  reflected  and  the  remainder 
went  on  to  the  auditor.  Thus,  the  sound  in  traversing  the  cohinm 
of  hot  air  lost  by  reflection  at  two  surfaces  and  reached  the  auditor 
diminished  in  intensitj'.  It  reached  the  auditor  with  diminished 
intensity  for  another  reason. 

The  column  of  warm  air  acted  like  a  lens.  The  effect  of  the 
column  of  air  was  not  like  that  of  the  ordinary  convex  lens, 
which  would  Ijring  the  sound  to  a  focus,  but  rather  as  a  diverging 
lens.  The  effect  of  a  convex  lens  would  have  been  obtained  had  the 
column  of  air  been  colder  than  that  of  the  surrounding  room.  Be- 
caus«'  the  air  was  warmer,  and,  thcrcl'ori-,  tin-  velocity  of  sound 
through  it  greater,  the  eflccl  was  to  cau.se  the  sound  in  passing 
through  the  cylindrical  colulun  to  diverge  even  more  rapidly  and 
to  reach  the  auditor  very  coiisiiierably  diiiiiiiislicd  in  iiilcM>ity. 
AVhich  of  these  two  effects  was  the  more  jjotcnt  in  <limiiii>liing  the 
souinl,  whether  the  loss  by  refltnlion  or  the  loss  by  Kn>-like  (lis|)er- 
sion  was  the  greater,  could  only  be  (leterminc<l  if  one  knew  the  tem- 
perature of  the  air  in  the  room,  in  I  he  lolimin.  and  I  he  diameter  of 


1?8  ARCHITECTURAL  ACOUSTICS 

tlu'  column.  It  is  sufficiont,  porliaps,  to  point  out  on  tlio  authority 
of  such  cniincnt  men  as  Dr.  licid  an.l  Mr.  Jeiniey  that  the  phenome- 
non is  a  real  one  and  one  to  be  avoided,  and  that  the  explanation  is 
ready  at  hand  and  comparatively  simple. 

It  is,  i)erhaps,  worlii  wiiile  pointing  out  tluit  in  both  of  the  above 
cases  there  was  a  good  deal  of  reverberation  in  the  room,  so  that 
any  considerable  diminution  in  the  intensity  of  the  sound  coming 
directly  from  the  speaker  to  the  auditor  resulted  in  its  being  lost 
in  the  general  reverberation.  Had  the  same  conditions  as  to  loca- 
tion of  speaker,  auditor,  column  of  warm  air  and  temperature 
occurred  out  of  doors  or  in  u  room  of  very  slight  reverberation  the 
effect  would  have  been  very  much  less  noticeable.  Nevertheless, 
great  irregularity  of  temperature  is  to  be  avoided,  as  the  above 
testimony  fairly  clearly  shows. 

The  above  also  suggests  another  line  of  thought.  If,  instead  of 
having  a  single  screen  of  great  temperature  difference  between 
speaker  and  auditor,  there  were  many  such  differences  in  tempera- 
ture, though  slight  in  amount,  the  total  effect  might  be  great.  This 
corrt\spon(ls,  in  the  effect  produced,  to  what  Tyndall  calls  a  "fioccu- 
leul  eoiulitiou  of  the  atmosphere"  in  his  discussion  of  the  trans- 
mission of  fog  signals.  Tyndall  points  out  that  if  the  atmosphere 
is  in  layers  alternately  warm  and  cold  sound  is  transmitted  with 
nnich  more  rajjid  diminution  in  intensity  than  when  the  atmosphere 
is  of  very  uniform  temperature.  This  phenomenon  is,  of  course, 
much  more  important  with  such  temperature  differences  as  occur 
out  of  doors  than  in  a  room,  but  it  suggests  that,  in  so  far  as  it  is  a 
perceptible  effect,  the  temperature  of  a  room  should  be  homogeneous. 
This  condition  of  homogeneity  is  best  secured  by  that  system  of 
ventilation  known  as  "distributed  floor  outlets."  It  has  the  addi- 
tional merit  of  being,  perhaps,  the  most  efficient  system  of  ven- 
tilation. 


SENSE  OF  LOUDNESS' 

It  will  be  showTi  here  that  there  is  a  sense  of  relative  loudness,  par- 
ticularly of  equality  of  loudness,  of  sounds  differing  greatly  in  pitch, 
that  this  sense  of  loudness  is  accurate,  that  it  is  nearly  the  same  for 
all  normal  ears,  that  it  is  independent  of  experience,  and  that,  there- 
fore, it  probably  has  a  pliysical  and  physiological  basis.  This 
investigation  has  been  incidental  to  a  larger  investigation  on  the 
subject  of  architectural  acoustics.  It  has  bearing,  however,  on 
many  other  problems,  such,  for  example,  as  the  standardization  of 
noises,  and  on  the  physiological  theory  of  audition. 

The  apparatus  used  consisted  of  four  small  organs  (Proc.  Am. 
Acad,  of  Arts  and  Sciences,  1906)'  so  widely  separated  from  each 
other  as  to  be  beyond  the  range  of  each  other's  influence.  Each 
organ  carried  seven  night-horn  organ  pipes  at  octave  intervals  in 
pitch,  (>4.  1'28,  256,  .  .  .  4006  vil)rations  per  second.  The  four  organs 
were  so  connected  electrically  to  a  small  console  of  seven  keys  that 
on  pressing  one  key,  any  one.  any  two.  any  three  or  all  four  organ 
pipes  of  the  same  pitch  would  sound  at  once,  —  the  comt)inalion  of 
organ  pipes  sounding  being  adjusted  by  an  assistant  and  unknown 
to  the  observer. 

In  other  parts  of  the  investigation  on  architectural  acoustics  the 
loudness  of  the  sound  emitted  by  each  of  the  twenty-eight  organ 
pipes  in  terms  of  the  niininnim  audible  sound  for  the  corresi)omling 
pitch  had  been  determined.  The  experiment  was  conducted  in  the 
large  lecture-room  of  the  Jefferson  Physical  Laboratory,  anil,  in 
I  Ik  manner  ex])lainf(l  elsewhere,  the  computation  was  made  for  the 
loudness  of  the  sound,  taking  into  account  the  shajie  of  the  roonj 
and  the  materials  employed  in  its  construction. 

The  experiment  consisted  in  adjusting  the  number  of  pipes  which 
were  souniling  or  in  choosing  from  among  the  i)ii)es  until  such  an 
adjustment  was  accomplished,  that,  to  an  observer  in  a  more  or  less 
remote  part  of  the  room  all  seven  notes,  when  souiuled  in  succession, 
.seemed  to  have  the  same  loudness.     .\s  tlie  pi|)es  of  the  same  pitch 

'  Contributions  from  llu-  Jc(Trnu)n  I'liysical  Ijilionitor>'.  vol.  viii,  1910. 
»  S.f  p.  84. 


130  SENSE  OF  L()rDXP:SS 

did  not  all  have  the  same  loudness,  it  was  possible  by  taking  various 
coinbinafions  to  make  this  atljustment  with  considerable  accuracy. 
Tiiis  statement,  however,  is  subject  to  an  amendment  in  that  all 
four  pipes  of  the  lowest  pitch  were  not  sufficiently  loud  anil  the 
faintest  of  the  highest  pitch  was  too  loud. 

There  were  ten  observers,  and  each  observer  carried  out  four  in- 
dependent experiments.  Speaking  broadly,  in  the  case  of  every 
observer,  the  four  independent  experiments  agreed  among  them- 
selves with  great  accuracy.  This  was  to  the  great  surprise  of  every 
observer,  each  before  the  trial  doubting  the  possibility  of  such  adjust- 
ment.   The  results  of  all  ten  observers  were  surprisingly  concordant. 

After  the  experiment  with  the  first  two  observers,  it  seemed 
possible  that  their  very  close  agreement  arose  from  their  familiarity 
with  the  piano,  and  that  it  might  be  that  they  were  adjusting  the 
notes  to  the  "balance"  of  that  particidar  instrument.  The  next 
observer,  therefore,  was  a  violinist.  Among  the  observers  there  was 
also  a  'cellist.  Lest  the  feeling  of  relative  loudness  should  come 
from  some  subconscious  feeling  of  vocal  effort,  although  it  is  diffi- 
cult to  see  how  this  coidd  extend  over  so  great  a  range  as  six  octaves, 
singers  were  tried  whose  voices  were  of  very  different  register.  Two 
of  the  observers,  including  one  of  the  pianists,  were  women.  Two 
of  the  observers  were  non-musical,  one  exceedingly  so. 

The  accompanying  table  gives  the  results  of  the  observations, 
the  energy  of  each  sound  being  expressed  in  terms  of  minimum 
audible  intensity  for  that  particular  pitch,  after  making  all  correc- 
tions for  the  reenforcement  of  the  sound  by  the  walls  of  the  room. 
The  observations  are  recorded  in  order,  the  musical  characteristic 
of  the  observer  being  indicated. 

Pitch  Frequency 


Observers 

64 

128 

256 

512 

1024 

2048 

409 

I .  Piano 

7.0(+)XlC*  1.7X10=4.4X10«   8.0X10«15.0X10«  9.6X10«4.5(- 

i.  Piano 

7.0+ 

1.7 

4.4 

11.2 

9.2 

12.0 

5.2- 

3.  Non-musical 

7.0+ 

1.7 

3.6 

8.9 

6.3 

9.6 

4.5- 

4.  Non-mus 

ical 

7.0+ 

1.7 

3.7 

7.7 

14.5 

14.4 

5.6- 

5.  Violin 

7.0+ 

1.7 

3.5 

11.7 

13.9 

8.0 

3.5- 

6.  Violin 

7.0+ 

1.7 

4.0 

11.4 

15.5 

15.2 

5.2— 

7.  'Cello 

7.0+ 

1.7 

4.2 

12.0 

13.4 

9.6 

5.1- 

8.  Tenor 

7.0+ 

1.7 

3.9 

13.3 

13.5 

10.5 

4.0- 

9.  Soprano 

7.0+ 

1.7 

4.7 

12.9 

17.0 

9.6 

5.4— 

10.  Piano 

7.0+ 

1.7 

3.5 

13.2 

14.5 

8.0 

4.9- 

7.0(+)  1.7  4.0  11.0  13.3  10.6  4.8- 


ARCHITFXTURAL  ACOUSTICS' 

CORRECTION-  OF  ACOUSTICAL  DIFFICrLTIKS 

v/N  the  completion  of  the  Fogg  Art  Museum  in  1895,  I  was  re- 
quested by  the  Corporation  of  Harvard  Fniversity  to  investigate 
the  subject  of  architectural  acoustics  with  the  end  in  view  of  cor- 
recting the  lecture-room  which  had  been  found  impracticable  and 
abandoned  as  unusable.  Later  the  planning  of  a  mw  lionie  for 
the  Boston  Synii)hony  Orchestra  in  Boston  widened  the  scope  of 
the  inquiry.  Since  then,  over  questions  raised  first  i)y  one  building 
and  then  another,  the  subject  has  been  under  constant  investigation. 

In  1900  a  series  of  articles,  embody  in. i^  llic  work  of  the  first  five 
years  and  dealing  with  the  subject  of  reverberation,  was  published 
in  the  American  Architect  and  also  in  the  Eiigin<'eriug  Becord.  The 
next  five  years  were  de\(>t('(l  to  the  extension  of  this  study  over  the 
range  of  the  musical  scale  and  the  residts  were  published  in  the  Pro- 
ceedings of  the  American  Academy  of  Arts  and  Scicncfs  in  190(i. 
Since  then  the  investigation  lias  been  with  reference  to  interference 
and  resonance,  the  effects  of  peculiarities  of  form,  and  the  causes 
of  variation  in  audibility  in  different  i)arts  of  an  auditorium.  These 
result >  will  be  published  in  anotlu^r  article  during  the  ensuing  year. 

The  i)rogress  of  this  experimental  investigation  has  been  guided 
in  practical  chaimels  and  greatly  rnriclied  by  the  experience  gaiui'd 
from  frequent  consultation  l)y  arcliilecl  s,  cillicr  for  purposes  of 
correcting  completed  buildings  or  in  the  prcjjaration  of  plans  in 
advance  of  construction.  Reserving  for  a  lalt-r  article  the  stimu- 
lating subject  of  advance  planning,  the  i)resent  article  is  devoteil 
to  liie  problems  involved  in  tiie  correction  of  comi)letcd  l)uildings. 
It  is  illiistrati'd  by  a  few  examples  which  are  especially  typical.  I 
desire  to  lake  this  ojiportunit}'  of  expressing  my  a]>])recialion  of 
IIk'  \<ry  cordial  ])ermission  to  use  this  material  given  by  the  archi- 
tects, Messrs.  McKini,  Mead  &  AVhite,  Messrs.  ( 'arrere  &:  Hastings, 
Messrs.  ("ram,  (Goodhue  &  l-'erguson,  and  Me»rs.  Allen  \:  Collens 

'  The  Architoclurul  Quarli-rly  uf  Ilurvuril  l'iiivvr.Hil\ ,  Munli,  iUli. 

»1 


13^2  AIUHITErTl'RAL  ACOUSTICS 

—  to  lln'Sf  ami  to  the  otlu-r  arcliitccts  whose  confidence  in  this  work 
has  rendered  an  extensive  experience  possible. 

The  practical  execution  of  this  work  of  correction  has  recently 
been  placed  on  a  firmer  basis  by  Mr.  C.  M.  Swan,  a  former  graduate 
stutlent  in  the  T'niversity  and  an  associate  in  this  work,  who  has 
taken  charge  of  a  dej)artment  in  the  H.  W.  Johns-]\ranville  Com- 
pany. I  am  under  obligations  to  him  and  to  this  company  for  some 
of  the  illustrations  used  below,  and  to  the  company,  not  merely  for 
having  i)Iaced  at  my  disposal  their  materials  and  technical  experi- 
ence, but  also  for  having  borne  the  expense  of  some  recent  investi- 
gations looking  toward  the  development  of  improved  materials, 
with  entire  privilege  of  my  making  free  publication  of  scientific 
results. 

It  is  proposed  to  discuss  here  only  such  corrective  methods  as 
can  be  enii)loyed  without  extensive  alterations  in  form.  It  is  not 
proposed  to  discuss  changes  of  dimension,  changes  in  the  position 
of  the  wall-surfaces  or  changes  in  ceiling  height.  It  is  the  purpose 
to  discuss  here  medicinal  rather  than  surgical  methods.  Such 
treatment  properly  planned  and  executed,  while  not  always  avail- 
able, will  in  the  great  majority  of  cases  result  in  an  entire  remedy 
of  the  difKculty. 

Two  old,  but  now  nearly  abandoned  devices  for  remedying  acous- 
tical difficulties  are  stretched  wires  and  sounding-boards.  The 
first  is  without  value,  the  second  is  of  some  value,  generally  slight, 
tlioii^li  occasionally  a  perceptible  factor  in  the  final  result.  The 
stretching  of  wires  is  a  method  which  has  long  been  employed,  and 
its  disfiguring  relics  in  nuniy  churches  and  court  rooms  proclaim  a 
diliiculty  which  they  are  powerless  to  relieve.  Like  many  other 
traditions,  it  has  been  abandoned  but  slowly.  The  fact  that  it  was 
wholly  without  either  foundation  of  reason  or  defense  of  argument 
made  it  difficult  to  answer  or  to  meet.  The  device,  devoid  on  the 
one  hand  of  scientific  foundation,  and  on  the  other  of  successful 
experience,  has  taken  varied  forms  in  its  application.  Apparently 
it  is  a  matter  of  no  moment  where  the  wires  are  stretched  or  in  what 
amount.  There  are  theatres  and  churches  in  Boston  and  New 
York  in  which  four  or  five  wires  are  stretched  across  the  middle  of 
the  room;    in  other  auditoriums  miles  on  miles  of  wire  have  been 


ACOUSTICAL  DIFFICULTIES 


133 


stretched;  in  both  it  is  equally  without  effect.  In  no  case  can  one 
obtain  more  than  a  quahfied  approval,  and  the  most  earnest  nega- 
tives come  where  the  wires  have  been  used  in  the  largest  amount. 
Occasionally  the  response  to  iiupiiries  is  that  "the  wires  may  have 
done  some  good  but  certainly  not  much,"  and  in  general  when  even 
that  qualified  approval  is  given  the  installation  of  the  wires  was 


F'l(i.  I.     Ciiliiig  of  ilmrcli.  .Sail  Jose,  t'iiliforiii:i.  showing  nn  ineffective  use  of  slrelched  wires. 


accoiiip;inici|  liy  some  dllicr'  cli.iiiui^  of  lnrin  i>v  ipccupiiiicy  to  which 
the  cretlil  should  be  given.  I  low  extensive  an  endeavor  is  .sometimes 
made  in  llie  use  of  slrclclicd  wires  is  sliowti  by  the  aeeomi)anying 
illustration  wliicli  sli<)W>  :i  >niail  section  of  I  lie  ceiling  of  a  church 
in  San  Jose,  Calil'iinii:!.  In  llii^  diunli  litlwciii  mir  aini  I  wo  mile-. 
of  wire  have  lu'cu  >lnl(licd  with  rrsull  iug  disfigurement,  and  wholly 
without  avail.  Tlic  (|Ucslion  is  being  taken  up  again  l>y  tlic  church 
for  renewed  I'il'ort . 


I'M  ARCHITECTrRAL  ACOUSTICS 

Aside  from  such  cuniiiliilivc  i-vidfiur  of  iiu-ttVclivciK-ss,  it  is  not 
dillicull  to  show  lliat  llK-if  is  no  pliysical  basis  for  the  device.  The 
sound,  whose  eclioes  these  wires  are  presumed  to  absorb,  scarcely 
affects  the  wires,  giving  to  them  a  vibration  wliich  at  most  is  of 
microscopical  magnitude.  If  tlic  string  of  a  violin  were  free  from 
the  body  of  llic  violin,  if  the  string  of  a  piano  were  free  from  the 


Fio.  2.     Congregational  Church,  Naugatuck,  Connecticut.    McKim,  Mead  and  White,  Architects. 

sounding-board,  if  the  string  of  a  harp  did  not  touch  the  thin  sound- 
ing-board which  faces  its  slender  back,  when  plucked  they  would 
not  emit  a  sound  which  could  be  heard  four  feet  away.  The  sound 
which  comes  from  each  of  these  instruments  is  communicated  to 
the  air  by  the  vibration  of  its  special  sounding-board.  The  string 
itself  cuts  through  the  air  with  but  the  slightest  communication  of 
motion.  Conversely  when  the  sound  is  in  the  room  and  the  string 
at  rest  the  vibrating  air  flows  past  it,  to  and  fro,  without  disturbing 


ACOUSTICAL  DIFFICULTIES 


135 


it,  and  consequently  without  itself  being  affected  by  reaction  either 
for  better  or  worse. 

The  sounding-board  as  a  device  for  correcting  acoustical  diffi- 
culties has  at  times  a  value;  but  unless  the  sounding-hoard  is  to 
be  a  large  one,  the  benefit  to  l)e  exi)ected  from  its  inslallatioii  may 
be  greatly  overrated.     As  I  his  |)articular  subject  calls  for  a  line  dI' 


Kiu.  J.    Hall  of  the  House  of  llepresfiitativ<vs,  Kliode  Isluiul  Stale  Capilol,  rrovidciic-e,  K.I. 
McKim.  Mcail  ami  W'liitc,  Arcliitit-ts. 

argument  very  different  from  that  of  tlie  main  body  of  the  present 
paper,  it  will  be  reserved  for  a  discussion  elsewhere,  where,  s|)aee 
permitting,  it  can  be  illustrated  l)y  i-xamples  of  various  forms 
accompanied  l)y  photographs  and  by  a  more  or  less  exhaustive 
discussion  of  their  relative  merits. 

The  auditorium  in  whose  special  behalf  tiiis  investigation  >tarteil 
seventeen  years  ago  was  tiie  lecture-room  of  the  Fogg  Art  Museum. 


13(5 


ARCHirKCTT RAL  ACOUSTICS 


Altlu)ii},'li  this  rouni  was  in  ;i  liirj^v  iiifasuic  rt-iiu'dit'il.  it  will  not  be 
taken  as  an  example.  Its  jjecnliarities  of  shape  wtic  sucli  that  its 
complete  relief  was  inherently  a  complicated  process.  While  this 
case  was  chn)nolof,'ically  the  first,  it  is  thus  not  suitable  for  an 
openinfT  illustration. 

.Vnionf,'  a   numixT  ol'   iiilcnslinfi;   i)roblems   in    advance   of   con- 
si  nicl  ion   the   linn   ot   McKim.   ^Fead   &   White   has  })ronght  .some 


Fk:.  i.     Dclaii.  Hall  cf  tin-  llcnisf  oi  l{r|)rrsi-Tiliilivcs,  Khodc  Island  State  Capitol. 
M<Kiiii,  Mead  and  While.  .Xrehitoets. 

interest inj^-  i)roblems  in  correction,  of  which  three  will  serve  ad- 
mirably as  examples  because  of  llicir  unusual  directness.  The  first 
is  that  of  the  Congregational  Church  in  Naugatuck,  Connecticut, 
shown  in  the  accomi)anying  illustration.  When  built  its  ceiling 
was  cylindrical,  as  now,  but  smooth.  Its  curvature  was  such  as  to 
focus  a  voice  from  the  platform  upon  the  audience,  —  not  at  a  point, 
but  along  a  focal  line,  for  a  cylindrical  mirror  is  astigmatic.     The 


fl 


ACOUSTICAL  DIFFICT'LTIES  137 

difficulty  was  evident  with  tlic  >i)i'iiking,  ImiI  iiuiy  he  (lescribed 
more  effectually  with  reference  to  the  singing.  The  position  of  tin- 
choir  was  behind  the  preacher  and  across  the  in;iin  axis  of  the 
church.  On  one  line  in  tlic  andiciicc,  crossing  tlic  cliiiicli  ()l)lif|iiely 
from  right  to  left,  the  soprano  voice  couhl  be  licard  coining  even 
more  sharply  from  the  ceiling  than  directly  IVotn  I  lie  singer,  'i'he 
alto  starting  nearer  the  axis  nl'  I  Ik-  (  IhhcIi  IkkI  I'or  il>  locus  a  hiu- 
crossing  the  church  less  ohliciucly.  'Ilic  i)hcnonK'na  were  similar  for 
the  tenor  and  the  bass  voices,  but  with  focal  lines  crossing  the 
church  obliquely  in  opposite  directions.  The  difficulty  was  in  a 
very  large  measure  remedied  by  coffering  I  he  ((iling,  as  shown  in 
the  illustration,  both  the  old  and  the  new  ceiling  being  of  i)laster. 
Ideally  a  larger  and  fleejier  coff<'ring  was  desiral)l('.  l)ut  the  solution 
as  shown  was  practical  and  the  result  satisfactory . 

The  hall  of  the  House  of  Kcprcscutal  ivcs  in  the  Hliodt-  Khind 
State  Capitol  illu^lralcd  aiiollicr  l\|ic  of  dillicully.  In  cousiilcring 
this  hall  it  is  necessary  to  bear  in  uu'nd  that  the  ])r()blcui  is  an  I'ssen- 
tially  different  one  from  thai  of  a  clnii-ch  or  Iccturc-room.  In  these 
the  speaking  is  from  a  raised  i)lalforni  and  a  fixed  ])osition.  In  a 
legislative  assembly  I  lie  -jieakiiig  is  in  I  he  uiain  from  I  he  lloor,  and 
may  be  from  any  part  of  llie  floor;  Ihe  speaker  stands  on  a  level 
with  his  fellow  members;  he  .stands  with  his  i)ack  to  a  part  of  the 
audience,  and  often  with  his  back  to  the  greater  ])art  of  his  audience; 
in  different  jyarU  of  Ihe  lion~e  the  s|)eaker  directs  his  voice  in  dif- 
ferent directions,  and  against  different  wall-surfaces.  In  this  hall 
the  walls  were  of  stone  to  ai)i)ro\iiuately  half  the  height  of  the 
room;  above  that  Ihey  were  of  stone  and  plaster.  The  ceiling  was, 
as  shown,  coffered.  The  dillii  iilty  in  this  room  was  with  that  part 
of  the  \-oiee  which,  crossing  Ihe  room  hansver.sely,  fell  on  Ihe  side 
walls.  With  the  sjjcaker  standing  on  Ihe  floor,  the  greater  volume 
of  his  voice  was  directed  upward.     The  -ound  striking  the  side  wall 

was  reflected  across  the  r i  In  llie  o|i|)osile  wall  and  l)ack  again, 

lo  and  fro.  inoiinl  iiig  gradually  until  it  re.ielnMl  the  ceiliui,'.  It  was 
there  retlcetcd  direclly  douu  upon  Ihe  audience.  'i'he  ceiling 
.slo|)e(l,  and  had  some  eur\alure.  but  llu'  curvature  was  not  such 
as  lo  produce  a  distinct  focusing  of  Ihe  sound.  During  Ihoe  re- 
flections Ihe  sound  mel  only  feel>ly  absorbeiil  surfaces  ami  there- 
fore  returned    to   the   auilielice   with   but    little   lo-s  of   illlen-il>.      Us 


i:js 


AR(Iiri'E(  irRAL  ACOUSTICS 


roturn  was  at  such  an  iiitt-rval  of  lime  as  to  result  in  great  confusion 
of  speech.  ()ni\-  thi>  fact  tliat  the  voice,  rising  at  different  angles, 
traveled  different  jjaths  and  therefore  returned  at  varying  inter- 
vals, i)revented  the  formation  of  a  distinct  echo.  The  difficulty 
was  remedied  in  tliis  case  hy  a  change  in  material  without  change 


Fig.  5.  Lecture-room,  Metropolitan  Museum  of  Art,  New  York. 
MoKim,  Mead  anil  White,  .\rchitects. 


of  form,  bj'  diminishing  the  reflecting  power  of  the  two  side  walls. 
This  was  done  by  placing  a  suitable  felt  on  the  plaster  walls  between 
the  engaged  columns,  and  covering  it  with  a  decorated  tapestry. 
Fortunately,  the  design  of  the  room  admitted  of  a  charming  exe- 
cution of  this  treatment.  It  is  interesting  to  note  that  this  treat- 
ment applied  to  the  lower  half  of  the  walls  would  not  have  been 
acousticallv  effective. 


ACOUSTICAL  DIFFICT'LTIES 


139 


The  lecture-room  of  the  Metropolitan  Museum  oi  Art  illus- 
trates the  next  step  in  complexity.  This  hall  is  a  semi-circular 
auditorium,  with  the  semi-circle  slightly  continued  hy  short, 
straight  walls.  As  shown  in  tlic  illustrations  the  ])latform  is  nearly, 
though  not  wholly,  witliin  a  i)r()ad  hut   shallow  recess.     The  body 


I'lu.  ti.     L<.-i  turc-roum,  Mrlropulilaii  MiiM-um  cif  Arl.  Nr«   >..rk, 
Mi-Kiiu.  Mtiul  uiul  Wliitc.  Anliil.cls. 

of  tlie  auditorium  is  .-.urmounteii  l)y  a  s|)liiTi(;d  ceiling  witli  >liurt 
cylindrical  extension  following  the  straight  side  walls.  In  tlie 
center  of  the  ceiling  is  a  flat  skylight  of  gla.ss.  In  lliis  room  the  re- 
verberation was  not  merely  excessive,  hut  it  resolved  itself  hy  focus- 
ing into  a  nndti|)le  echo,  the  components  of  which  followed  each 
other    with    great    rapidity    hut    were    distinctly    .sepju-ahle.      The 


140  AlU  IIITECTITRAL  ACOUSTICS 

nuiiiluT  (li.stinguislial)li'  variiHl  in  differiMit  parts  of  tin-  hall.  Seven 
were  ilislingiiislial)le  al  cerlain  i)arts.  A  detailed  discussion  of  this 
is  not  ajjpropriate  in  the  present  paper  as  it  concerns  rather  the 
subject  of  calculation  in  advance  of  construction.  To  improve  the 
acoustics  the  ceiling  was  coffered,  the  limiting  depth  and  dimensions 
of  this  cofTeriiig  being  determined  in  large  measure  by  the  dimen- 
sions of  the  skylight.  The  semi-circular  wall  at  the  rear  of  the 
auditorium  was  li-aii.vrornicd  inlo  panels  wliich  wi're  filled  with 
fell  over  which  was  slretclicd  huria])  as  shown  in  the  second  illus- 
tration. The  result  was  the  result  assured, — the  reduction  of  the 
disturbance  to  a  single  and  highly  localized  echo.  This  echo  is 
audible  only  in  the  central  seats  —  two  or  three  seats  at  a  time  — 
and  moves  about  as  the  speaker  moves,  but  in  symmetrically  opposite 
direction.  Despite  this  residual  effect,  and  it  should  be  noted  that 
this  residual  effect  was  predicted,  the  result  is  highly  satisfactory  to 
Dr.  I'ldward  Rot)inson,  the  Dii'ector  of  the  Museum,  and  the  room  is 
now  used  with  comfort,  whereas  it  had  been  for  a  year  abandoned. 

It  .should  be  borne  in  mind  that  "perfect  acoustics"  does  not 
mean  the  total  elimination  of  reverberation,  even  were  that  possible. 
Loudness  and  reverljcration  are  almost,  though  not  quite,  projjor- 
tional  qualities.  The  result  to  be  sought  is  a  balance  between  the 
two  ((ualities,  dependent  on  the  size  of  the  auditorium  and  the  use 
to  which  it  is  to  be  applied. 

Geometrically  the  foregoing  cases  are  comparatively  simple.  In 
each  case  the  room  is  a  simple  space  bounded  by  plane,  cylindrical 
or  spherical  surfaces,  and  these  surfaces  simplj^  arranged  with  refer- 
ence to  each  other.  The  simplicity  of  these  cases  is  obvious.  The 
complexity  of  other  cases  is  not  always  patent,  or  when  jiatent  it  is 
not  obvious  to  a  luerely  casual  inspection  how  best  the  problem 
should  be  attacked.  A  large  number  of  cases,  however,  may  be 
handled  in  a  practical  manner  by  regarding  them  as  connecting 
spaces,  each  with  its  own  reverberation  and  pouring  sound  into  and 
receiving  sound  from  the  others.  An  obvious  case  of  this  is  the 
theatre,  where  the  aggregate  acoustical  propertj'  is  dependent  on 
the  space  behind  the  proscenium  arch  in  which  the  speaker  stands, 
as  well  as  on  the  space  in  front  of  it.  In  another  sense  and  to  a  less 
degree,  the  cathedral,  with  its  chancel,  transept  and  nave  may  be 


Fi(i.  7.    Di-sign  for  St.  I'lturs  Cnllu-ilrnl.  D.-lroil.    Crnin.  (lotxlhuf  and  Ferguson.  .Vrchilocts. 


142  ARC  IinECTniAL  ACOUSTICS 

rt'fiiirded  as  a  caso  of  conncotcd  sj)aC('s.  The  problem  certainly  takes 
on  a  simpler  aspect  when  so  attacked.  An  extreme  and  purely  hy- 
pothetical case  would  he  a  deep  and  wide  auditorium  with  a  very 
low  ceiling,  and  with  a  stage  recess  deep,  high  and  reverberant,  in 
fact  such  a  cjise  as  might  occur  when  for  special  purposes  two  very 
<Iifl"erent  rooms  are  thrown  together.  In  such  a  case  the  reverbera- 
tion calculated  on  the  l)asis  of  a  single  room  of  the  combined  volume 
and  the  combined  absorbing  power  would  yield  an  erroneous  value. 
The  speaker's  voice,  especially  if  he  stood  back  some  distance  from 
the  oj)eiiing  between  the  two  rooms,  would  be  lost  in  the  production 
of  reverberation  in  its  own  space.  'J'lie  total  resulting  sound,  in  a 
confused  mass,  would  be  propagated  out  over  the  auditorium.  Of 
course  this  is  an  extreme  case  and  of  imusual  occurrence,  but  by  its 
very  exaggeration  serves  to  illustrate  the  point.  In  a  less  degree 
it  is  not  of  infrequent  occurrence.  It  wjis  for  this  reason,  or  rather 
through  the  experience  of  this  eflfect,  although  only  as  a  nice  refine- 
ment, that  the  Boston  Symphony  Orchestra  has  its  special  scenery 
stage  in  Carnegie  Hall,  and  for  this  that  Mr.  Damrosch  in  addition 
moved  his  orchestra  some  little  distance  forward  into  the  main 
auditorium  for  his  concerts  in  the  New  Theatre. 

A  cathedral  is  a  good  example  of  such  geometrical  comijlication. 
still  further  complicated  by  the  variety  of  service  which  it  is  to 
render.  It  must  be  adajited  to  speaking  from  the  pulpit  and  to 
reading  from  the  lectern.  It  must  be  adapted  to  organ  and  vocal 
nmsic,  and  occasionally  to  other  forms  of  service,  though  generally 
of  so  minor  importance  as  to  be  beyond  the  range  of  appropriate 
consideration.  Most  cathedrals  and  modern  large  churches  have 
a  reverberation  which  is  excessive  not  only  for  the  spoken  but  also 
for  a  large  portion  of  the  musical  service.  The  difficulty  is  not 
peculiar  to  any  one  type  of  architecture.  To  take  European  ex- 
amples, it  occurs  in  the  Classic  St.  Paul  in  London,  the  Romanesque 
DiU'liani.  the  Basilican  liouianesciue  Pisa,  the  Italian  Gothic  Flor- 
ence, and  the  English  (iothic  York. 

The  most  interesting  example  of  this  type  has  been  Messrs.  Cram, 
Goodhue  &  Ferguson's  charming  cathedral  in  Detroit,  especially 
interesting  because  in  the  process  of  correcting  the  acoustics  it  was 
possible  to  carry  to  completion  the  decoration  of  the  original  design. 


Via.  8.    St.  Paul's  Cathedral.  Detroit.    Cram,  Goodhue  and  Ferguson,  .\rchitccts. 


U4  AlU'IIITKCTrHAL  A( OlSTICS 


rty 


riie  nav«-.  modt-raloly  narrow  in  the  clcroslory.  was  l)roa(l  hi'low 
throufrli  ils  i-xtiMision  by  side  aisles.  It  niiglit  fairly  be  regariled 
as  two  simply  eonneeted  spaces.  The  lower  space,  when  there  was 
;i  full  :Micliciicc.  was  aluiiiilaiilly  al)sorl)cnl  ■.  Ilu-  clcrcslory,  Ihoujili 
with  wood  ceiling,  wius  not  absorbent.  All  hough  their  conil)ine(l 
reverberation  was  great,  it  was  not  so  great  as  alone  to  j)roduce  the 
aclnal  etlVet  obtained.  Absorbing  material  in  the  form  of  a  felt, 
highly  efficient  acoustically,  was  placcii  in  the  i)atiels  on  tlie  ceiling, 
'riic  i>riginal  arcliilcci  iiral  design  by  Mr.  Cram  (Fig.  7)  showed  the 
ceiling  decorated  in  colors,  and  this  though  not  a  ])art  of  the  original 
construction  was  carried  out  on  the  covering  of  the  felt,  with  a  re- 
sult highly  satisfactory  both  acoustically  and  architecturally.  The 
transept,  also  high  and  reverberant,  was  similarly  treated,  as  was' 
also  the  central  tower  which  was  even  higher  than  the  rest  of  the 
church.  As  a  mailer  of  fact  the  results  at  first  attained  were  satis- 
factory only  with  an  audience  filling  at  least  three-quarters  of  the 
seats,  the  condition  lor  which  it  was  planned.  'Hie  treatment  was 
subsequenll\-  extended  to  the  lower  levels  in  order  that  the  cathedral 
might  be  serviceable  not  merely  for  the  normal  but  for  the  occa- 
sionally small  audience.  The  chancel  did  not  need  and  did  not 
receive  any  sjiecial  treatment.  It  was  highly  suitable  to  the  musical 
service,  and  being  at  the  back  of  both  the  pulpit  and  the  lectern  did 
not  greatly  affect  that  portion  of  the  service  which  called  for  dis- 
tinctness of  enunciation. 

It  may  be  remarked  in  j)assing  that  the  lectern  is  almost  invari- 
ably a  more  difficult  problem  than  the  pulpit.  This  is  in  part  be- 
cause reading,  with  the  head  thrown  slightly  forward,  is  more 
difficult  than  speaking;  because,  if  the  lectern  is  sufficiently  high 
to  permit  of  an  erect  position  it  screens  the  voice;  because  a  speaker 
without  book  or  manuscript,  seeing  his  audience,  realizes  his  dis- 
tance and  his  difficulties;  and  finally,  because  the  pulpit  is  generally 
higher  and  against  a  column  whereas  the  lectern  stands  out  free  and 
unsupi)orled. 

The  auditorium  which  has  received  the  greatest  amount  of  dis- 
cussion recently  is  the  New  Theatre  in  New  York.  Had  it  been  a 
commercial  proposition  its  acoustical  quality  would  have  received 
but  passing  notice.     As  an  institution  of  large  purpose  on  the  part 


ACOUSTICAL  DIFFICT'I/riES  145 

of  the  Founders  il  recvived  a  coriTspoiidiiifrly  Iar<;i'  atlciilion.  As 
an  institvition  of  generous  purpose,  without  liope  or  (h'sire  for  finan- 
eial  return,  il  was  a])propriate(l  hy  I  he  jjublie,  and  received  (lie 
persistent  eritieism  which  seems  llie  usual  reward  for  >u(li  under- 
takings. The  writer  was  consulted  only  after  the  completion  of 
the  buildiuf--.  hut  its  acoustical  difficulties  can  he  discussed  ade- 
quately only  in  the  light  of  its  inili;d  pi'ogranniie. 

It  was  part  of  the  original  i)rogramnie  submitted  to  Messrs. 
Carrere  &  Hastings  that  the  building  should  be  used,  or  at  least 
should  be  adapted  to  use  for  opera  as  well  as  for  ilrama.  In  this 
respect  it  was  to  bear  to  the  ISIetropolitan  the  position  which  the 
Opera  Comique  in  Paris  bears  to  the  ()j)era.  This  idea,  with  its 
corollary  features,  influenced  the  early  design  .nul  ^liows  in  the 
completed  structure. 

Il  was  also  a  part  of  the  initial  plan  tli.it  there  >lionid  be  two 
rows  of  boxes,  something  very  unn>ual  in  thcalrc  loiistrnction. 
'Hiis  was  a  i)ro(ligal  use  of  .space  and  magnified  the  Imilding  in  .ill 
its  ilimensions.  Later,  but  not  until  after  the  building  was  nearly 
completed,  the  upper  row  of  bo.xes  was  abandoned,  and  the  galU-ry 
thus  created  was  devoted  to  foyer  chairs.  As  the  main  walls  were 
by  this  time  erected,  tlic  gallery  wa>  limited  in  depth  to  the  boxes 
and  their  antechambers.  It  thus  resulted  that  this  level,  which  is 
ordinarily  occupied  by  a  gallery  of  great  value,  is  of  small  ca))acity. 
Notwithstanding  this  the  New  'I'heatre  seats  twenty-three  hun- 
dred, while  the  usual  theatre  seats  but  little  more  than  two-thirds 
that  number. 

The  necessity  of  providing  t wenlx-three  connnodious  boxes,  all 
in  the  first  tier,  of  which  none  should  be  so  near  the  stage  as  to  be 
distinctly  inferior,  determined  a  large  circle  for  their  front  and  ft>r 
the  fi'ont  of  all  the  galleries.  Thus  not  nirrcl\-  .iic  I  in-  seats,  which 
are  orilinarily  I  lie  best,  seats,  far  from  tlii'  stage,  but  the  great  hori- 
zontal scale  thus  necessitated  leads  arehilecturally  to  a  correspond- 
ingly great  vertical  scale.  I'he  row  of  boxes  and  the  foyer  balcony 
above  n<it  merely  determined  the  scale  of  the  auditorium,  but  al>o 
presenfe<l  at  the  back  of  their  shallow  dei)th  a  concave  wall  whieii 
focused  file  rellectcd  .-.ound  in  the  center  of  the  auditorium. 

Finallv,  il  should  be  borne  in  mind  Ihat  while  the  acoustical 


14(5  AlltlllTECTURAL  ACOUSTICS 

clfinauds  in  :i  tlu-iifrc  are  greater  than  in  almost  any  oilier  lyi)e  of 
auditorium,  because  of  the  great  modulation  of  the  voice  in  dra- 
matic action,  the  New  Theatre  was  undertaking  an  even  more 
than  usually  difficult  task,  that  of  presenting  on  the  one  hand  the 
older  dramas  with  their  less  familiar  and  more  difficult  phrasing, 
and  on  the  other  the  more  subtle  and  delicate  of  modern  plays. 


Kk;.  '.>.     Intorior,  the  New  Theatre,  New  York  City.     Carrere  and  Hastings,  Architects. 

The  conventional  type  of  theatre  construction  is  fairly,  though 
only  fairly,  well  adapted  to  the  usual  type  of  dramatic  perfornuince. 
The  New  Theatre,  with  a  very  difficult  type  of  performance  to 
present,  was  forced  by  the  conditions  which  surrounded  the  project 
to  depart  from  the  conventional  type  far  more  radically  than  was 
perhaps  at  that  time  realized. 

Here,  as  usual  in  a  completed  building,  structural  changes  and 
large  changes  of  form  were  impossible,  and  the  acoustical  difficulties 


ACOUSTICAL  1  )I  FFICULTIES 


147 


of  the  auditorium  ccjuld  \)v  renu'died  only  l)y  iiKJiirction.  The 
method  1).\  whicli  a  very  considerable  improvement  was  attained 
is  shown  by  a  comparison  of  the  line  drawing  (Fig.  10)  with  the  plio- 
tograpii  of  the  interior  of  the  theatre  as  originally  couiplcted.  The 
boxes  were  changed  from  the  first  to  the  second  Ivvvl,  lii'ing  inter- 
changed with  the  foyer  chairs,  wliilc  I  lie  excessive  height  of  the 
main  l)o(ly  of  tlie  auditorimn  was  reduced  by  means  of  a  canopy 
surrounding   tlic  (•culral   chandelier.     This   ingenious   and   iiol    dis- 


Fiu.  lU.      The  New  Theatre.  New  York  City,  .showing  Canopy  ami  Changed  Hoses. 

pleasing  substitute  for  the  recommended  lowering  of  the  ceiling  was 
proi)o.sed  by  ^Nfr.  Hastings,  although  of  course  only  as  a  means  to 
an  end.  The  canopy  is  oval  in  plan,  following  the  outline  of  the 
oval  panel  in  the  ceiling,  its  longer  axis  being  transverse.  Its  major 
and  minor  liori/.oulal  dimensions  are  70  f«'et  and  40  feet.  Its 
effective  lowering  of  the  height  of  the  ceiling  is  •20  fe<-t.  A  moment's 
consideration  will  show  that  its  effective  area  in  i)reventing  the 
ceiling  echo  is  greater  than  its  acliuil  dimensions,  particularly  in 


148  ARCHITECTrHAL  ACOUSTICS 

tlu'  (iiriK-tion  of  its  minor  axis.  Tlic  iin])rovenient  hrouglit  al)oul 
by  this  was  pronouncecl  and  satisfactory  to  the  Founders.  The 
di.stances,  however,  were  still  too  great,  even  visually,  for  the  type 
of  dramatic  performance  for  whicli  the  theatre  was  primarily  in- 
tended, and  such  use  was  therefore  discontinued.  The  New  Tlieatre 
is  nuich  better  adapted  to  opera  than  to  dramatic  performances, 
and  it  will  he  a  matter  of  great  regret  if,  with  its  charming  solution 
of  many  (llllicull  arc  hilccltiral  jjiolilcnis.  it  is  not  restored  to  such 
dignifietl  j)urpose. 

The  last  and  very  satisfactory  exami)le  is  lliat  of  the  Chapel  of 
the  I'nion  Theological  Seminary  of  ^Messrs.  Allen  &  Collens.  Its 
interesting  feature  is  thai  the  corrective  treatment  was  applied  in 
the  process  of  construction.  It  is  further  interesting  as  an  example 
of  a  Irealnient  which  is  not  merely  inconspicuous,  hut  is  entirely 
intlislinguishable.  The  pholograpii  witlioiit  explanation  is  the  best 
evidence  of  this  (p.  149). 

The  above  examples  have  been  chosen  from  many  score  as  typical 
of  the  principles  involved.  In  each  case  the  nature  of  the  difficvdty 
has  been  stated  and  the  method  emi)loyed  in  its  correction,  or  at 
least  its  special  feature  very  brieflj'  described.  The  remainder  of 
I  lie  i)apcr  will  he  devoted  to  a  discussion  of  the  j)rinciples  involved 
in  acoustical  correction  and  in  ])resenting  the  results  of  some  recent 
exi>eriments. 

Iti  discussing  the  above  exam])les,  especially  the  fii'st  and  the 
third,  tlic  Congregational  Church  in  Naugatuck,  and  the  lecture- 
room  oi'  the  Metropolitan  Mu,seiun  of  Art,  consideration  had  to  be 
given  to  the  effect  of  the  geometrical  shape  of  the  room.  This 
aspect  of  the  problem  of  architectural  acoustics  constitutes  a  sub- 
ject so  large  that  a  separate  paper  must  be  devoted  to  its  adequate 
treatment.  It  involves  not  merely  simple  reflection  })ut  inter- 
ference and  diffraction,  as  well  as  the  far  from  simple  subject  of  the 
pro])agation  of  soimd  jiarallel  to  or  nearly  parallel  to  the  jilane  of 
an  audience.  It  has  been  the  object  of  special  investigation  during 
tlic  ])ast  six  years.  This  investigation  has  recently  come  to  a  suc- 
cessful issue  and  will  probably  be  jniblished  in  full  during  the  en- 
suing year.  It  is  suitable  that  it  should  receive  separate  pul)lication 
for,  as  it  concerns  shape,  it  is  of  more  value  for  calculation  in  ad- 


I'll..  II.     (  liiip.j.  I  iiiiiii  riiii.li)«iral  Siiiiliiary,  Nrw  Viirk  (  il.\ .     Alien  iiiul  t 


1.50  AIU'IIITPXTrRAL  ACOUSTICS 

vance  of  construction  than  in  the  correction  of  conii)Icted  buildings. 
It  nnist  here  suffice  to  merely  indicate  the  nature  of  the  results. 

When  soiuul  is  produced  in  a  confined  auditorium  it  spreads 
si)herically  from  the  source  until  il  reaches  the  audience,  the  walls, 
or  I  lie  ceiling.  It  is  there  in  part  absorbed  and  in  part  reflected. 
The  part  which  is  reflected  ret ra verses  the  room  until  it  meets 
another  surface.  It  is  again  in  part  absorbed  and  in  i)arl  reflected. 
This  process  continues  until,  after  a  greater  or  less  number  of 
reflections,  the  sound  becomes  of  negligible  intensity.  Tluis  at  aii\- 
one  lime  and  at  any  one  point  in  the  room  there  are  many  sounds 
crossing  each  other.  In  a  very  simple  auditorium,  such  as  a  simple 
rectangular  room  with  plain  walls  and  ceiling,  this  process  is  not 
difficult  to  follow,  eitlier  step  l)y  stej),  or  In-  large,  but  entirely 
adequate,  generalizations.  When  the  conditions  are  more  compli- 
cated it  is  more  diflficult  to  analyze;  it  is  also  more  liable  to  be  a 
vitally  significant  factor  in  the  problem.  That  it  has  heretofore 
been  inadequately  discussed  has  arisen  from  the  failure  to  take  into 
consideration  the  phenomenon  of  diffraction  in  the  propagation  of 
a  sound  nearly  parallel  to  an  absorbing  audience,  the  phenomenon 
of  diffraction  in  reflection  from  an  irregular  surface,  and.  above  all, 
tlie  phenomenon  of  interference.  The  first  of  these  three  considera- 
tions is  of  primary  importance  in  calculating  the  intensity  of  the 
sound  which  has  come  directly  from  the  source,  in  calculating  the 
effect  of  distance  in  the  audience,  and  in  calculating  the  relative 
loudness  on  the  floor  and  in  the  gallery,  and  at  the  front  and  at  the 
back  of  the  gallery.  The  second  consideration  enters  into  the  cal- 
culation of  the  path  of  the  sound  after  reflection  from  any  broken 
or  irregular  surfaces.  The  third  is  a  factor  of  the  utmost  impor- 
tance when  the  sounds  which  are  crossing  at  any  point  in  the  audi- 
torium are  of  comparable  intensity  and  have  traveled  paths  of  so 
nearly  equal  length  that  they  have  originated  from  the  same  ele- 
ment.   This  latter  calls  for  a  more  elaborate  explanation. 

In  both  articulate  speech  and  in  music  the  source  of  sound  is 
rapidly  and  in  general,  abruptly  changing  in  pitch,  quality,  and 
loudness.  In  music  one  pitch  is  held  during  the  length  of  a  note. 
In  articulate  speech  the  unit  or  element  of  constancy  is  the  syllable. 
Indeed,  in  speech  it  is  even  less  than  the  length  of  a  syllable,  for  the 


ACOUSTICAL  DTFFICITI.TIES  151 

open  vowel  sound  wliich  forms  the  Ixjcly  of  u  syllable  usually  has  a 
consonantal  opening  and  closing.  During  the  constancy  of  an  ele- 
ment, either  of  music  or  of  speech,  a  train  of  sound-waves  spreads 
spherically  from  the  source,  just  as  a  train  of  circular  waves  spreads 
outward  from  a  rocking  boat  on  the  surface  of  still  water.  Different 
portions  of  this  train  of  spherical  waves  strike  different  surfaces  of 
the  auditorium  and  are  reflected.  After  such  reflection  they  begin 
to  cross  each  other's  paths.  If  their  paths  are  so  diflferent  in  length 
that  one  train  of  waves  has  entirely  passed  before  the  other  arrives 
at  a  particular  point,  the  only  phenomenon  at  that  point  is  pro- 
longation of  the  sound.  If  the  space  between  the  two  trains  of 
waves  be  suflBciently  great  the  effect  will  be  that  of  an  echo.  If 
there  be  a  number  of  such  trains  of  waves  thus  widely  sjjaced,  the 
effect  will  be  that  of  multiple  echoes.  On  the  other  hand  if  the  two 
trains  of  waves  have  traveled  so  nearly  equal  paths  that  they  over- 
lap, they  will,  dependent  on  tin-  difference  in  length  of  the  paths 
which  they  had  traveled,  either  reenforce  or  mutually  destroy  each 
other.  Just  as  two  equal  trains  of  water-waves  crossing  each  other 
may  entirelj'  neutralize  each  other  if  the  crest  of  one  and  the  trough 
of  the  other  arrive  together,  so  two  sounds,  coming  from  the  same 
source  in  crossing  each  other  may  produce  silence.  This  phenom- 
enon is  called  interference  and  is  a  common  phenomenon  in  all 
types  of  wave  motion.  ()i  course  this  phenomenon  has  its  comple- 
ment. If  the  two  trains  of  water-waves  so  cross  that  the  crest  of 
one  coincides  with  the  crest  of  the  other  and  trough  with  trough, 
the  effects  will  be  added  together.  If  the  two  sound-waves  be  simi- 
larly retarded,  the  one  on  the  other,  their  effects  will  also  be  added. 
If  the  two  trains  of  waves  be  equal  in  intensity,  the  combined  in- 
tensity will  be  quadruple  that  of  either  of  the  trains  separately,  iis 
above  exjjlained,  or  zero,  depending  on  their  relative  retardation. 
The  effect  of  this  phenomenon  is  to  produce  regions  in  an  audito- 
rium of  loudness  and  regions  of  comparative  or  even  comi)lete  silence. 
It  is  a  partial  explanation  of  the  so-called  deaf  regions  in  an  audi- 
loriuni. 

It  is  not  difficult  to  observe  this  phenomenon  directly.  It  is 
difficult,  however,  to  measure  and  record  the  phenomenon  in  such 
a  nuumer  as  to  permit  of  an  accurate  chart  of  the  result.     Without 


152  ARCHITECTURAL  ACOUSTICS 

going  into  the  details  of  the  metliod  employed  the  result  of  these 
nieiisurements  for  a  room  very  similar  to  the  Congregational  Church 
in  Naugatuck  is  sliown  in  the  accompanying  chart.  The  room 
experimented  in  was  a  simple  rectangular  room  with   plain  side 


Fig.  \i.  Distribution  of  intensity  on  the  head  level  in  a  room 
with  a  barrel-shaped  ceiling,  with  center  of  curvature  on  the 
floor  level. 


walls  and  ends  and  with  a  barrel  or  cylindrical  ceiling.  The  ceiling 
of  the  room  was  smooth  like  the  ceiling  of  the  Naugatuck  Church 
before  it  was  coffered.  The  result  is  clearly  represented  in  Fig.  12, 
in  which  the  intensity  of  the  sound  has  been  indicated  by  contour 
lines  in  the  manner  employed  in  the  drawing  of  the  Geodetic  Survey 


ACOUSTICAL  DIFFICULTIES  153 

maps.  The  phenomenon  indicated  in  these  diagrams  was  not 
ephemeral,  but  was  constant  so  long  as  the  source  of  sound  con- 
tinued, and  repeated  itself  with  almost  perfect  accuracy  day  after 
day.  Nor  was  the  j)]u'nonu>non  one  wliich  could  be  observed  merely 
instrumenlally.  To  an  observer  moving  about  in  the  room  it  was 
quite  as  striking  a  phenomenon  as  the  diagrams  suggest.  At  the 
points  in  the  room  indicated  as  high  maxima  of  intensity  in  the 
diagram  the  sound  was  so  loud  as  to  be  disagreeable,  at  other  i)oints 
so  low  as  to  be  scarcely  audible.  It  should  be  added  that  this  dis- 
tribution of  intensity  is  with  the  source  of  sound  at  the  center  of 
the  room.  Had  the  source  of  sound  been  at  one  end  and  on  the  axis 
of  the  cylindrical  ceiling,  the  distribution  of  intensity  would  still 
have  been  bilaterally  synmietrical,  but  not  symmetrical  about  the 
transverse  axis. 

As  before  stated  a  full  discussion  of  this  phase  of  the  subject  is 
reserved  for  another  paper  which  is  now  about  read}'  for  publication. 

In  the  second,  in  the  fourth,  and  in  part  in  the  third  of  the  above 
examples  the  acoustical  diflTiculty  was  that  of  excessive  reverberation. 

If  a  sound  of  constant  pitch  is  maintained  in  an  auditorium, 
though  only  for  a  very  brief  time,  the  sound  spreading  directly 
from  the  source,  together  with  the  sounil  wliicli  has  been  reflected, 
arrives  at  a  steady  state.  The  intensity  of  the  sound  at  any  one 
point  in  the  room  is  then  the  resultant  of  all  the  superposetl  sounds 
crossing  at  that  point.  As  just  shown,  the  nuitual  interference  of 
these  superposed  sounds  gives  a  distribution  of  intensity  which 
shows  pronounced  maxima  and  minima.  However,  the  ])r()l)ablc 
intensity  at  any  point,  as  well  as  the  aggregate  intensity  over  the 
room,  is  the  sum  of  the  components.  Whatever  the  distribution  of 
maxima  and  minima  the  state  is  a  steady  one  so  long  as  the  source 
continues  to  sound.  The  steady  condition  in  tlic  room  is  mkIi  lliat 
the  rate  of  absorption  of  the  souikI  is  ((iikiI  to  llu-  rate  of  emi>>ioii 
by  the  source. 

If  after  this  steady  state  is  established  I  lie  source  is  aliruptly 
checked,  the  ditlVreiit  trains  of  waves  will  continue  their  jouru<y, 
the  maxima  and  mininui  shifting  positions.  Ultimately,  the  .soimd 
will  ceiuse  to  be  audible,  having  diminished  in  inleiisily  until  it  has 
pa.s.sed  below  what  aurisls  call  the  "threshold  of  audibility."     The 


154  ARCHITECTURAL  ACOUSTICS 

chiralion  of  iuidihilify  after  the  source  hivs  ceased  is  thus  dependent 
upon  tlie  initial  intensity,  upon  tlie  absorbing  material,  and  upon 
the  location  of  that  absorbing  material  with  reference  to  the  several 
trains  of  waves.  In  special  cases  the  position  of  the  absorbing  ma- 
terial is  a  matter  of  the  utmost  importance,  but  in  many  cases  the 
aggregate  result  may  be  computed  on  the  basis  of  the  total  absorbing 
power  in  the  room. 

The  prolongation  of  the  sound  in  an  auditorium  after  the  source 
has  ceased  I  have  ventured  to  call  reverberation,  and  to  measure  it 
mmierically  by  the  duration  of  audibility  after  the  abrupt  cessation 
of  a  .source  which  has  producetl  an  average  intensity  of  sound  in  the 
room  equal  to  one  million  times  minimum  audible  intensity.  This 
is  an  ordinary  condition  in  actual  occurrence. 

In  the  1900  papers  published  in  the  Engineering  Record  and  the 
American  Architect,  this  subject  of  reverberation  was  discussed  at 
great  length,  and  it  was  there  shown  how  it  might  be  measured  and 
indeed,  how  it  might  be  calculated  in  advance  of  construction.  In 
addition  to  the  formula  many  coefficients  of  absorption  were  de- 
termined, such  data  being  absolutely  necessary  to  the  reduction  of 
the  subject  to  an  exact  science.  This  work  related  to  sounds  having 
a  pitch  an  octave  above  middle  C. 

But  it  was  of  course  obvious  that  the  acoustical  quality  of  an 
auditorium  is  not  determined  by  its  character  with  reference  to  a 
single  note.  The  next  series  of  papers,  published  in  1906,  therefore 
extended  the  investigation  over  the  whole  range  of  the  musical  scale 
giving  data  for  many  materials  and  wall-surfaces,  and  rendering  a 
more  complete  calculation  possible.  At  the  conclusion  of  these 
papers  it  was  shown  how  the  reverberation  of  an  auditorium  should 
be  rejjresented  by  a  curve  in  which  the  reverberation  is  plotted 
against  the  pitch  and  by  way  of  illustration  a  particular  case  was 
shown,  that  of  the  large  lecture-room  in  the  Jefferson  Physical 
Laboratory,  both  with  and  without  an  audience.  This  curve  is 
reproduced  in  the  accompanying  diagram  (Fig.  13). 

In  the  process  of  investigating  an  auditorium  such  a  curve 
should  be  drawn  as  definitive  of  its  initial  condition  and  then  in  the 
determination  of  the  treatment  to  be  employed  similar  curves 
should  be  drawn  representing  the  various  alterations  proposed  and 


ACOUSTICAL  DIFFICULTIES 


155 


taking  into  consideration  the  location  of  the  surfaces,  their  areas 
and  the  nature  of  the  proposed  treatment.  The  diagram  (Fig. 
14)  shows  the  result  of  this  computation  for  the  more  inter- 
esting of  the  above  examples,  St.  Paul's  Cathedral,  Detroit.  In 
this  diagram  curves  are  drawn  plotting  the  reverberation   of   the 

10 


^^^1  ~- 

V 

—           o 

c. 


c, 


Cj 


c. 


c.       c, 


Fig.  13.  Curves  showing  the  reverberation  in  the  lecture- 
room  of  the  Ji'lTrrsoii  I'hy.sical  l.alMirnlory  without  an 
auJienee  and  witli  iin  audience  lilling  all  the  seat.s. 

ciitlicdral  in  its  original  condition,  empty,  and  with  a  Ihree-ijiiartcrs 
audience,  and  with  a  full  audience,  and  again  after  its  acou>tical 
correction  also  empty,  witli  ;i  three-quarters  audience,  and  with  a 
fidl  audience. 

Reprints  of  the  pajx-rs  just   mcnlioned  were  iiiailed  at   the   time 
to  all  members  of  the  American  Institute  of  Architects.     l)ui)licales 


156 


ARCHITECTURAL  ACOUSTICS 


will  gladly  bo  sent  to  any  one  who  may  be  interested  in  the  further 
perusal  of  the  subject. 

Brief  mention  has  l)een  made  of  the  dependence,  in  special  cases, 
of  the  efficiency  of  an  absorbing  material  on  its  positions  in  an  au- 
ditorium.   For  example,  in  the  room  whose  distribution  of  intensity 

10 


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\ 

\ 
\ 

\ 

N 

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y 

X 

X 

v\ 

N 

x* 

y 

\ 
\ 
\ 
\ 

\ 

L                     \                     \ 

\                     \                           > 

A    \ 
*  \   ^ 

\ 

\\  \  \ 

;-\ 

K 

-2--^ 

"^  X 

x^ 

/: 

/ 

-3  -- 

.  ^ 

\j 

s;^ 

\3 

/ 

''J 
-4 

^ 

^^4- 

O.        O,        Cj        c.        c,        c.        c, 

Fig.  14.  Curves  showing  the  reverberation  in  St.  Paul's 
Cathedral,  Detroit,  before  (1',  2',  3',  4')  and  after  (1,  2, 
3,  4)  corrections,  empty  and  with  a  one-quarter,  one- 
half,  three-quarter  and  full  audience. 

was  shown  in  Fig.  12,  the  absorbing  material  would  have  much 
greater  efficiency  in  reducing  the  reverberation  if  placed  so  as  to 
include  maxima,  than  if  so  placed  as  to  include  minima.  That  this 
would  be  true  is  obvious.  The  magnitude  of  the  effect,  however,  is 
not  so  clear,  for  the  maxima  and  minima  shift  as  the  sound  dies 


ACOUSTICAL  DIFFICULTIES 


157 


away.     It  was   therefore  submitted   to  an  accurate   experimental 
investigation.     The  results   are  shown   in   the  adjacent    diagram. 


/ 

\ 

/ 

\ 

1.0 
.9 
.8 
.7 

Q 

/ 

\ 

\ 

j 

\ 

1 

2 
1 

> 

\ 

/ 

1 
/ 

N 

K^- 

.5 
4 

\a 

( 

\ 

\ 

3 
\ 

^ 

V 

3 

1 

'// 

\ 

2 

J 

/ 

\ 

1 

^ 

-y 

o, 


c, 


c. 


c> 


c. 


c. 


Kio.  15.  .Sliowing  lliv  ri-liitivc  rtjiiu-iuy  of  fi-ll  in  tlilliT- 
eiit  parts  of  a  ri>oiii  liiiviiiK  a  harrcl  it-iliiiK.  Curve  1. 
uuriiiul  al)»orhiiit;  ixmcr;  ("urvu  i.  absorliin);  jxjwfr  in 
the  (TiiliT  of  tin-  room;  Curve  3.  ulisortiiiiK  iM>wrr  at 
the  .siilc  of  I  hi-  room.     Cj  i.s  miiliilr  C,  iJU. 

Fig.  15.     In  tins  diagram  tlie  curve  marked  1  >liows  hy  its  vertical 

ordinatcs  the  iiornial  ('(licii'iicy  of  a  very  lii^'iiiy  aliMirlu-nt  felt.     If 


158 


ARCHITECTTTIAL  ACOUSTICS 


so  placed  in  the  room  as  to  include  on  its  surface  the  maxima  of 
intensity  of  the  sound  it  had  an  effective  absorbing  power  as  shown 
in  Curve  2,  a  truly  remarkable  increase  over  its  normal  value. 
Curve  3  shows  the  effic-iency  of  the  same  felt  when  placed  against 
the  side  wall.    It  there  included  more  maxima  than  minima  for  the 

1.0 


.9 


.5 


.3 


^ 

/ 

1 

/ 

""n 

\ 

1- 

N 

\ 

/ 

\ 

\\ 

^^ 

4 

1 

v^ 

^ 

c, 


c, 


c< 


c. 


c, 


Fig.  16.   Absorbing  power  of  various  kinds  of  felt  as  de- 
fined in  the  text.    C3  is  middle  C,  256. 


lower  notes,  but  more  minima  than  maxima  for  the  higher  notes, 
with  a  resulting  efficiency  curve  which  is  very  irregidar. 

The  following  experiments  were  performed  for  the  H.  W.  Johns- 
Manville  Company  in  the  search  for  an  efficient  absorbing  material 
and  an  effective  method  of  treatment.  The  absorbing  eflBciency  of 
felt  is  dependent  on  the  flexibility  of  the  mass  as  a  whole  and  on  its 
porosity.     It  is  not  in  large  measure  dependent  on  the   material 


ACOUSTICAL  DIFFICULTIES 


159 


employed,  except  in  so  far  as  the  nature  of  that  material  determines 
the  nature,  and  therefore  the  closeness,  of  the  felting  process.  The 
same  materials,  therefore,  might  very  well  have  either  a  very  high 
or  a  very  low  ahsorljing  efficiency,  depending  entirely  upon  the 
process  of  manufacture.    The  nature  of  the  material  is  here  specified, 

1.0 


.9 


.8 


.1 


,<<^ 

^ 

I 

f 

\ 

^ 

i 

\ 

^ 

i 

1 

_^ 

^ 

c, 


c. 


c, 


Fio.  17.  Effect  of  air  space  behind  felt.  Curve  1,  felt  in 
contact  with  the  wall;  Curves  2,  3.  and  \,  felt  at  dis- 
tamrs  of  i.  4,  uiid  (i  inches  from  the  wall. 

not  with  tlie  idea  tlial  it  iilouc  can  (Iftcnuine  tlie  (|uality,  Kill  iniTfly 
as  an  additional  j)iece  of  information.  In  addition  to  this,  in  each 
case  the  ratio  of  tlic  solid  iii.itnial  to  tlic  free  .s|)ace  is  given;  l>ul 
even  this  does  not  define  in  full  the  essential  conditions.  The  al)- 
sorbing  power  is  determined  not  merely  hy  tiie  ratio  of  the  air  space 
to  the  solid  material,  but  by  the  size  of  the  pores  and  by  the  elns- 


lUO 


ARCHITECTLTIAL  ACOUSTICS 


ticity  and  viscosity  of  the  mass  as  a  whole.  In  Fig.  16  Curve  1  is 
a  hair  felt,  the  one  alluded  to  above  as  of  exceptional  efficiency. 
The  fraction  of  its  total  volume,  which  is  solid  material,  is  0.12. 
Ciu-ve  2  is  a  mixture  of  hair  felt  and  asbestos,  whose  solid  portion  is 


Fig.  18.  Curves  showing  the  effect  on  absorbing  power 
of  membrane  covering.  Curve  1,  felt;  Curve  2,  burlap 
cemented  with  silicate  of  soda;  Curve  3,  light  mem- 
brane as  described;  Curve  4,  heavy  membrane  as  de- 
scribed; lower  Curve  3,  light  membrane  alone;  lower 
Curve  i,  heavy  membrane  alone. 

0.19  of  its  total  volume.  Curve  3  is  a  felt  wholly  of  asbestos  f" 
thickness,  whose  solid  portion  is  0.33  of  its  total  volume.  In  this 
latter  the  asbestos  fiber  is  felted  to  an  asbestos  cloth  which  serves 
to  strengthen  it  greatly.  Curve  4  is  for  an  asbestos  felt  without 
reenforcement.    That  a  considerable  fraction  of  its  absorbing  power 


ACOUSTICAL  DIFFICULTIES  Kil 

is  tliie  to  its  elastic  yii-lding  jis  a  whole  is  shown  by  its  rather  sharp 
maxima. 

The  curves  in  Fig.  17  show  the  effect  of  holding  the  felt  at  differ- 
ent distances  from  the  wall.  In  each  case  it  was  held  on  a  wire 
grating.  Curve  1  is  when  the  felt  is  as  near  the  wall  as  the  grating 
would  permit,  perhai)s  within  a  quarter  of  an  inch  of  the  wall. 
Curve  2  is  when  the  IVll  was  held  at  a  distance  of  two  inches;  Curve 
;5  at  four  inches;  and  Curve  4  at  sL\  inches  from  the  wall.  It  is 
evident  that  there  is  a  slight  gain  from  an  air  space  behind  the  felt, 
but  it  is  alkO  evident  that  this  gain  is  so  shght  as  to  be  entirely 
incommensurate  with  the  cost  of  construction  and  its  loss  in  dur- 
ability. 

The  Curves  in  Fig.  18  show  the  efficiency  of  various  coverings. 
Curve  1  is  the  normal  exjjosed  efficiency  of  the  felt  above  referred 
to.  Curve  2  is  its  efficiency  when  covered  by  burlap  attached  by 
silicate  of  soda.  This  covering  was  so  sized  as  to  be  practically 
impervious,  but  was  in  contact  with  and  a  part  of  the  felt.  Curves  3 
and  4  show  the  efficiency  of  coverings  which  are  not  in  contact  with 
the  felt,  but  wliicli  are  .stretched.  Both  coverings  are  impervious,  — 
3  relatively  light,  4  heavy.  Number  3  weighs  0.87  ounces  to  the 
square  foot;  number  4  weighs  2.58  ounces  to  the  square  foot.  The 
materials  of  which  these  coverings  are  made  have  no  bearing  on  the 
question,  and  would  be  misleading  if  stated.  The  really  significant 
factors  are  their  weight,  the  tension  with  which  they  are  stretched, 
their  elasticity,  and  their  viscosity.  The  weight  of  the  several 
coverings  hjis  been  stated;  the  other  factors  can  be  defined  best  by 
means  of  their  independent  absorbing  j)owers.  Lower  curves  3  and  4 
indicate  the  ab.sorbing  |)()wcr  of  the  niemljrane  coverings  alone. 
It  is  interesting  to  note  that  the  diaphragm  which  has  by  itself  the 
least  absorbing  power  has  tlic  grcat.^l  absorbing  jwwer  when 
combined  with  th(>  fell.  This  is  l)y  no  means  a  i)aradox.  H  is 
exactly  the  result  which  could  l)e  i)redieted  by  application  of  the 
simplest  of  physical  princijjles. 


THEATRE  ACOUSTICS' 

ViTRUVirs,  De  Architectura,  Liher  V,  Cap.  VIII.    (De  locis  con- 
sonantibus  ad  theatra  eligendis.) 

"  All  this  being  arranged,  we  must  see  with  even  greater  care  that  a 
position  has  been  taken  where  the  voice  falls  softly  and  is  not  so  reflected 
as  to  produce  a  confused  effect  on  the  ear.  There  are  some  positions  offer- 
ing natural  obstructions  to  the  projection  of  the  voice,  as  for  instance  the 
dissonant,  which  in  Greek  are  termed  n.aTr]xolvTK\  the  circumsonant,  which 
with  them  are  named  TrepiTjxoiVres ;  and  again  the  resonant,  which  are  termed 
avTTi]XO^''Ti%.    The  consonant  positions  are  called  by  them  o-iTijxoicTes. 

The  dissonant  are  those  places  in  which  the  sound  first  uttered  is  carried 
up,  strikes  against  solid  bodies  above,  and,  reflected,  checks  as  it  falls  the 
rise  of  the  succeeding  sound. 

The  circumsonant  are  those  in  which  the  voice  spreading  in  all  direc- 
tions is  reflected  into  the  middle,  where  it  dissolves,  confusing  the  case 
endings,  and  dies  away  in  sounds  of  indistinct  meaning. 

The  resonant  are  those  in  wliidi  the  voice  comes  in  contact  with  some 
solid  substance  and  is  reflected,  producing  an  echo  and  making  the  case 
terminations  double. 

The  consonant  are  those  in  which  the  voice  is  supported  and  strength- 
ened, and  reaches  the  ear  in  words  which  are  clear  and  distinct." 

This  is  an  admirable  analysis  of  the  problem  of  theatre  acoustics. 
But  to  adapt  it  to  modern  nomenclature,  we  must  substitute  for  the 
word  dissonance,  inlerforence;  for  the  word  circunisonance.  rever- 
beration; for  the  word  resonance,  echo.  For  consonance,  we  liave 
unfortunately  no  single  term,  but  the  conception  is  one  which  is  fun- 
damental. 

It  is  po.ssible  that  in  the  above  translation  and  in  the  following 
interpretation  I  iiave  read  into  the  text  of  Vitruvius  a  dcfinitcness  of 
concei)tion  and  an  accord  with  modern  science  which  his  language 
only  fortuitously  permits.  If  so,  it  is  erring  on  the  better  side,  and  is 
but  a  reasonable  latitude  to  take  under  the  circumstances.  The  only 
passage  whose  interpretation  is  open  to  serious  (lucstion  is  that  rc- 

'  Tlif  .ViniTirati  Anliitwt,  viil.  rlv.  p.  ii'i. 
las 


I(i4  THEATRE  ACOUSTICS 

latinj;  to  dissonant  i)laces.  If  Vitruvius  knew  that  the  superposition 
of  two  sounds  could  produce  silence,  and  the  expression  "opprimit 
inseqiientis  vocis  elationem"  permits  of  such  interpretation,  it  must 
stand  as  an  observation  isolated  by  many  centuries  from  the  modern 
knowledge  of  the  now  familiar  phenomenon  of  interference. 

Interferenxe 

Interference  is  a  phenomenon  common  to  all  types  of  wave  motion. 
The  best  introduction  to  its  discussion  is  by  reference  to  water-waves 


Fio.  2.  Greek  Theatre  at  the  University  of  California.    Mr.  John  Galen  Howard,  Architect. 

and  in  particular  to  an  interesting  example  of  tidal  interference  on 
the  Tongking  Peninsula.  The  tide  of  the  Pacific  Ocean  enters  the 
Chinese  Sea  through  two  channels,  one  to  the  north  of  the  Philippine 
Islands,  between  Luzon  and  Formosa,  and  the  other  through  the 
Sulu  Archipelago  between  Mindanao  and  Borneo.  The  northern 
channel  is  short  and  deep;  and  the  tide  enters  with  very  little  re- 
tardation. The  other  channel,  although  broad,  is  shallow,  tortuous, 
and  broken  by  many  small  islands ;  and  the  tide  in  passing  through 
is  nuicli  retarded.  The  two  tides  thus  entering  the  Chinese  Sea  pro- 
duce an  effect  which  varies  from  point  to  point.  At  one  port  on  the 
Tongking  Peninsula,  these  tides  are  so  retarded  relatively  to  each 
other  as  to  be  six  hours  apart.  It  is  high  tide  by  one  when  it  is  low 
tide  by  the  other.   It  also  so  happens  that  at  this  point  the  two  tides 


THEATRE  ACOUSTICS  165 

are  equal.  Being  equal  and  exactly  opposite  in  phase,  they  neutralize 
each  other. 

Because  tidal  waves  are  long  in  comparison  with  the  bodies  of 
water  in  which  they  are  propagated,  their  interference  phenomena 
are  obscure  except  to  careful  analysis,  ^^^len,  liowever.  the  waves 
are  smaller  than  the  space  in  which  they  are  being  propagated,  the 
interference  system  becomes  more  marked,  more  complicated,  and 
more  interesting.  Under  such  circumstances,  there  may  be  regions 
of  perfect  quiet  near  regions  of  violent  disturbance. 

Subjecting  the  parallel  to  a  more  exact  statement,  whenever  two 
water-waves  come  together  the  resulting  disturbance  at  any  instant 
is  equal  to  the  algebraic  sum  of  the  disturbances  which  each  would 
produce  separately.  If  their  crests  coincide,  the  joint  effect  is  equal 
to  the  sum  of  their  sei)arate  effect.  If  crest  and  trough  coincide,  their 
joint  effect  is  the  ditference  between  them.  If  their  relative  retarda- 
tion is  intermediate,  a  wave  results  which  is  intermediate  between 
their  sum  and  their  difference  and  whose  time  of  maximum  does  not 
occur  simultaneously  with  the  niaxinuim  of  either  of  the  components. 

The  i)lienomenon  is  one  which  may  be  produced  accurately  on 
any  scale  and  with  any  type  of  wave  motion.  Thus  sound  consists 
of  waves  of  alternate  condensation  and  rarefaction  in  the  air.  If  two 
trains  of  .sound-waves  cross  each  other  so  that  at  a  given  point  con- 
densation in  the  two  trains  arrive  simultaneously,  the  rarefactions 
will  al.so  arrive  simultaneously,  and  the  total  dislurl)ance  is  a  train 
of  waves  of  condensation  and  rarefaction  equal  to  the  sum  of  the  two 
components.  If  one  train  is  retarded  so  that  its  condensations  coin- 
cide with  the  ()ther's  rarefactions,  llie  disturbance  produced  is  the 
difference  between  that  whicii  would  be  produced  by  the  trains  of 
waves  separately.  Just  as  a  tidal  wave,  a  storm  wave,  or  a  ri[)i)le 
may  be  made  to  separat<'  and  recross  by  some  obstacle  nnuul  \\  lii(  h 
it  diffracts  or  from  whicii  it  is  reflected,  and  reeoinbining  proiluee 
regions  of  violent  and  regions  of  mininuun  disturbances,  so  sound- 
waves may  be  diffracted  or  reflected,  and  recomi)ining  after  travel- 
ling different  paths,  produce  regions  of  great  loudness  aiul  regions  of 
almost  complete  silence.  In  general,  in  an  auditorium  the  phenom- 
enon of  interference  is  produced  not  l)y  the  crossing  of  two  trains  of 
waves  only,  but  by  the  crossing  of  many,  reileeted  from  the  various 


IGG  THEATRE  ACOUSTICS 

walls,  from  the  ceiling,  from  the  floor,  from  any  obstacle  whatever 
in  the  room,  while  still  other  trains  of  waves  are  produced  by  the 
diffraction  of  the  sound  around  columns  and  pilasters. 

A  source  of  sound  on  whose  steadiness  one  can  rely  is  all  that  is 
necessary  in  order  to  make  the  phenomenon  of  interference  obviovis. 
A  low  note  on  a  pure  toned  stop  of  a  church  organ  will  serve  the 
purpose  admiral)ly.  The  observer  can  satisfy  himself  that  the  note 
is  sounding  steadily  by  remaining  in  a  fixed  position.  As  soon,  how- 
ever, as  he  begins  to  move  from  this  position  by  walking  up  and  down 
the  aisle  he  will  observe  a  great  change  in  loudness.  Indeed,  he  may 
find  a  position  for  one  ear  which,  if  he  closes  the  other,  will  give  al- 
most absolute  silence,  and  this  not  far  from  positions  where  the 
sound  is  loud  to  the  extent  of  being  disagreeable.  The  observer  in 
walking  about  the  church  will  find  that  the  phenomenon  is  compli- 
cated. It  is,  however,  by  no  means  random  in  its  character,  but 
definite,  pennanent,  and  accurate  in  its  recurrence,  note  for  note. 
Tlie  phenomenon,  while  difficult,  is  by  no  means  impossible  of  experi- 
mental investigation  or  of  theoretical  solution.  Indeed,  this  has  been 
done  with  great  care  in  connection  with  the  study  of  another  prob- 
lem,—  that  of  the  Central  Criminal  Court  Room  in  London  known  as 
Old  Bailey.  The  full  primary  explanation  of  the  methods  and  results 
of  this  general  investigation  would  be  inappropriately  long  in  an 
article  dealing  with  the  acoustics  of  theatres;  for  while  interference 
is  a  factor  in  every  auditorium,  it  is  on  the  whole  not  the  most 
seriously  disturbing  factor  in  theatre  design. 

The  subject  of  interference  would  not  have  been  given  even  so 
extended  a  discussion  as  this  in  a  paper  dealing  with  theatres  were 
it  not  that  recently  there  has  been  proposed  in  Germany  a  fonn  of 
stage  setting  known  as  the  Kuppel-horizont  for  sky  and  horizon 
effects,  to  accompany  the  Fortuny  system  of  stage  lighting,  in  which 
interference  may  be  a  not  inconsiderable  factor  unless  guarded 
against.  The  Fortuny  system,  which  in  the  opinion  of  some  com- 
petent judges  is  an  effective  fonn  of  stage  lighting,  consists  primarily 
in  the  use  of  indirect  illumination,  softened  and  colored  by  reflection 
from  screens  of  silk.  As  an  adjunct  to  the  system,  and  in  an  en- 
deavor to  secure  a  considerable  depth  to  the  stage  without  either 
great  height  or  an  excessive  use  of  sky  and  wing  flies,  a  cupola  is 


THEATRE  ACOUSTICS 


167 


recommended  to  go  with  the  Fortuny  lighting  as  shown  in  the  ac- 
companying figures  taken  from  the  pubHcations  of  the  Berliner  Alle- 
gemeine  Electriciiats  Gesellschuft.  In  Figs.  3  and  4,  the  cupohi  is 
shown  in  section  and  in  i)l:iii.  Liglits  A  and  B  illuminate  the  interior 
of  the  cupola;  C  and  K  light  the  area  of  the  stage  on  which  the  prin- 


CU^TAiN  DRaPCR  t 


OKCMtSTlA  ?  r 


PLAN 


Figs.  3  and  4.    Sorlion  niul  plan  of  tlir  Kiippel-Horijx)!!! 
with  Fortuny  systriii  of  liKliliiiR. 

cipal  action  occurs.  Cloud  (fTccts,  either  stationary  or  moving,  are 
])rojected  on  the  surface  of  the  cupola  i)y  a  stereoi)ticon.  The  great 
advantage  claimed  for  this  form  of  stage  setting  is  the  more  natural 
arrangement  of  stage  properties  wliidi  it  makes  possible,  and  the 
elimination  of  numerous  (lies.  On  tiie  other  hand  there  is  .sonu'  criti- 
cism that  this  lighting  results  in  an  unnatural  silhouetting. 


1(>8 


THEATRE  ACOUSTICS 


So  (K-taiIrd  an  exi)lanatioii  of  the  diagrams  and  the  purpose  of  the 
several  parts  is  necessitated  by  the  fact  that  it  is  as  yet  an  unfamiHar 
device  in  this  country.  It  has  been  introduced  recently  in  a  number 
of  theatres  in  Germany,  although  I  believe  not  elsewhere,  unless 
possibly  in  one  theatre  in  England.  It  has  been  called  to  my  atten- 
tion by  Professor  Baker  as  a  possible  equipment  of  the  theatre  which 


Fig.  5.  Interference  system  for  tennr  C  in  the  Kuppel-Horizont, 
having  a  tliirty-six  foot  proscenium  opening.  The  intensity 
of  sound  is  represented  by  contour  lines,  the  maximum  vari- 
ation being  forty-seven  fold. 


is  proposed  for  the  dramatic  department  of  Harvard  University,  and 
it  is  reasonable  to  regard  it  as  a  probable  factor  in  theatre  design  in 
other  countries  than  Germany. 

In  Fig.  5  is  plotted  the  interference  system  established  in  this 
space,  on  a  standing  head  level  of  five  feet  from  the  floor  of  the  stage, 
by  a  sustained  note  tenor  C  in  pitch.  The  intensity  of  the  sound  is 
indicated  by  contour  lines  very  much  as  land  elevation  is  indicated 
on  the  maps  of  the  Geodetic  Survey.  In  this  plot,  account  has  been 
taken  of  the  sound  reflected  from  the  cupola  and  from  the  floor.  No 
account  has  been  taken  of  the  reflection  from  the  walls  of  the  main 
auditorium  since  this  would  be  a  factor  only  for  sounds  prolonged 
beyond  the  length  of  any  single  element  in  articulate  speech.  Even 
in  the  case  of  a  very  prolonged  sound  the  modification  of  the  inter- 


THEATRE  ACOUSTICS  l(i!) 

ference  system  of  the  stage  and  cupola  by  the  rest  of  the  auditorium 
would  be  very  slight. 

The  interference  system  on  the  stage  in  question  being  deter- 
mined wholly  by  the  floor  and  cupola,  it  may  be  computed,  and  in 
the  preparation  of  tlie  chart  was  computed,  by  the  so-called  method 
of  images.  The  sound  reflected  from  the  floor  comes  as  from  a  virtual 
image  as  far  beneath  the  floor  as  the  mouth  of  the  speaker  is  above 
it.  Each  of  these  produce  real  images  by  reflection  from  the  interior 
of  the  cupola.  Bearing  in  mind  that  these  real  inuiges  show  the 
phenomenon  of  diffraction  and  some  astigmatism,  and  taking  into 
account  the  phase  of  the  sound  as  determined  by  reflection  and  by 
distance,  the  calculation  is  laborious  but  not  difficult.  It  involves 
but  the  most  familiar  processes  of  geometrical  optics. 

The  disturbing  effect  of  this  interference  system  is  not  so  great 
when  the  speaker  is  well  in  front  of  the  center  of  curvature  of  the 
cupola,  and  of  course  it  is  almost  always  more  or  less  broken  by  the 
stage  properties,  as  indicated  in  Figs.  :5  and  4.  Nevertheless,  it  is 
well  to  bear  in  mind  that  the  (piarler  s])liere  form,  as  indicated  in  the 
diagrams,  is  neither  neces.sary  from  the  standpoint  of  illumination 
nor  desirable  from  the  standpoint  of  acoustics.  Acoustically  a  flatter 
back  with  sharper  curvature  above  and  at  the  sides  is  preferable. 

It  shovdd  be  repeated  that  the  interference  .system  is  established 
only  when  the  tones  are  sustained,  in  this  case  over  one-tenth  of  a 
second,  and  is  more  of  an  annoyance  to  the  actor  on  the  stage  than 
to  the  audience.  With  shorter  tones  it  becomes  an  echo,  and  in  this 
form  is  quite  as  annoying  to  the  audience  as  to  the  actor.  It  should 
be  added  that  the  interference  changes  with  change  of  pitch,  but 
preserves  extreme  maxima  and  minima  for  a  central  jjosition  in  a 
spherical  or  partly  spherical  surface.  Finally  in  music,  since  sus- 
tained tones  occur  more  than  in  si)eech.  the  interference  is  more  dis- 
turbing. The  efl'ecl  of  >uch  >])lierical  stage  recesses  on  nnisic  is 
shown  i>y  those  otiicrwisc  inmsually  cxcflhiit  auditorimiis.  Orches- 
tra Hall  in  Chicago,  and  llie  Concert  Hall  at  Willow  (Irovc  Park 
near  I'hiladelphia. 


170  THEATRE  ACOUSTICS 

Re\'erberation" 

" Circumsonant  places"  were  rare  and  almost  wliolly  negligible 
difficulties  in  Greek  and  Roman  theatres.  However,  they  were  com- 
mon in  tlie  temples,  and  were  even  more  pronounced  in  some  of  the 
older  Roman  palaces.  It  must  have  been  in  the  experience  of  such 
conditions,  wholly  foreign  to  the  theatre  of  which  he  was  writing, 
that  Vitruvius  made  this  portion  of  his  analysis  of  the  acoustical 
l)roblem.  Given  the  fundamental  form  of  the  Greek  theatre,  it  re- 
quired no  special  consideration  and  little  or  no  skill  to  avoid  such 
(lifrKulties.  However,  this  is  not  true  of  the  modern  theatre,  in  which 
excessive  reverberation  is  more  often  the  defect  than  any  other 
factor. 

If  a  sound  be  produced  briefly  in  a  wholly  empty,  wholly  closed 
room,  having  perfectly  rigid  walls,  it  will  be  reflected  at  each  inci- 
dence with  undiminished  intensity,  and,  travelling  to  and  fro  across 
the  room,  will  continue  audible  almost  indefinitely.  Of  course  no 
theatre,  ancient  or  modern,  satisfies  these  conditions  and  the  sound 
loses  at  each  reflection,  diminishing  in  intensity,  until  in  the  course  of 
time  it  crosses  what  the  experimental  psychologist  calls  the  "thresh- 
old of  audibility."  In  the  Greek  theatres  the  duration  of  audibility 
of  the  residual  sound  after  the  cessation  of  a  source  of  ordinary  loud- 
ness was  never  more  than  a  few  tenths  of  a  second;  in  a  modern 
theatre  it  may  be  several  seconds.  The  rapidity  with  which  the 
sound  dies  away  depends  on  the  size  of  the  theatre,  on  its  shape,  on 
the  materials  used  for  its  walls,  ceiling,  and  furnishings,  and  on  the 
size  and  distribution  of  the  audience.  The  size  and  shape  of  the 
theatre  determines  the  distance  travelled  by  the  sound  between 
reflections,  while  the  materials  determine  the  loss  at  each  reflec- 
tion. No  actual  wall  can  be  perfectly  rigid.  Wood  sheathing, 
plaster  on  wood  lath,  plaster  on  wire  lath,  plaster  applied  directly 
to  the  solid  wall,  yield  under  the  vibrating  pressure  of  sound  and 
dissijKite  its  energy.  Even  a  wall  of  solid  marble  yields  slightly, 
transmitting  the  energy  to  external  space  or  absorbing  it  by  its  own 
internal  viscosity. 

Absorptions  by  the  walls  and  other  objects  in  the  process  of  reflec- 
tion, including  in  this  transmission  through  all  openings  into  outer 


THEATRE  ACOUSTICS  171 

space  as  ec|uivalcnt  to  total  ahsoq^tion  —  boundary  conditions  in 
other  words  —  are  ])racti('aliy  alone  (o  he  credited  with  the  dissolu- 
tion of  tiie  residual  sound.  I5ul  \ilruvius'  statement  that  the 
sound  "is  reflected  into  the  luiddie.  where  it  dissolves"  challenges 
completeness  and  at  least  tiie  mention  of  another  factor,  which, 
because  of  its  almost  infinitesimal  inii)ortance,  woidd  otherwise  be 
passed  without  connnent. 

Assimiing,  what  is  of  course  impossible,  a  closed  room  of  ab- 
solutely rigid  and  perfectly  reflecting  walls,  a  sound  once  started 
would  not  continue  forever,  for  where  the  air  is  condensed  by  the 
passing  of  the  wave  of  sound,  it  is  heated,  and  where  it  is  rarefied,  it 
is  cooled.  Between  these  uiUMiually  heated  regions  and  between 
them  and  the  walls,  there  is  a  continual  radiation  of  heat,  with  a  re- 
sulting dissipation  of  available  energy.  In  the  course  of  time,  but 
only  in  the  course  of  a  very  long  time,  the  sound  would  even  thus 
cease  to  be  of  audible  intensity.  This  form  of  dissijnition  might  well 
be  called  in  the  language  of  Vitruvius  "solvens  in  medio":  but.  in- 
stead of  being  an  important  faddi-,  il  is  an  entirely  negligible  factor 
in  any  actual  auditorium. 

Practically  the  rapidit\'  with  whicii  tin'  sound  is  absorlied  is  de- 
pendent solely  on  the  nature  of  the  reflecting  surfaces  and  the  length 
of  the  path  which  the  sound  nuist  traverse  between  reflections,  the 
latter  depending  on  the  shajjc  and  si/e  of  the  auditorium.  It  was 
shown  in  a  series  of  papers  i)ut)lished  in  The  American  Architect  in 
1900,'  and  in  another  paper  published  in  the  Proceedings  of  the  Amer- 
ican Academy  of  Arts  and  Sciences  in  1906,'  that,  given  the  jilan^  of 
an  auditorium  and  the  material  of  which  it  is  composetl,  it  is  ])ossible 
to  calculate  with  a  very  high  degree  of  accm'acy  the  rate  of  decay  of 
a  sound  in  the  room  and  the  duration  of  its  audibility.  In  the  first  of 
the  above  papers  there  was  given  the  comi)l(tc  theory  of  llie  subject, 
together  with  tables  of  experimentally  determinetl  coelHcients  of  ab- 
sori)tion  of  sound  for  practically  all  the  materials  that  enter  into 
auilitorium  construction,  for  sounds  lia\ing  a  ])ileh  one  octave  aliove 
middle  C  (vibration  fr<'(|uene_\  .Jl'2).  In  the  second  of  tlie  alici\e 
papers  llicre  were  gi\cn  the  eoeilieients  of  ab'-oiption  of  liuilding 
material--  foi-  tli<'  wholr  laiige  of  the  nuisical  scale. 

'  >i'  piiKr  (l!i.  •  Iliiil. 


M^i 


THEATRE  ACOUSTICS 


In  the  careful  design  of  a  room  for  musical  jjurjioses,  the  problem 
obviously  must  include  the  whole  range  of  the  musical  scale,  at  least 
seven  octaves.  It  is  not  so  obvious  that  the  study  must  cover  so 
great  a  range  when  the  primary  use  is  to  be  with  the  spoken  voice. 
The  nearest  study  to  architectural  acoustics  is  the  highly  develojjed 
science  of  telephony,  and  in  this  it  is  a])parently  sufficient  for  much 
of  the  work  to  adapt  the  theory  and  design  to  the  single  frequency  of 
800,  api)roximately  A  in  the  second  octave  above  middle  C.   But  for 


Fig.  6.    The  Little  Theatre,  New  York.    Ingalls  and  Hoffman,  Architects. 

some  problems  the  in\'estigatioii  must  be  extended  over  a  consider- 
able range  of  pitch.  Similarly  experience  in  the  architectural  prob- 
lem shows  that  with  some  of  the  materials  entering  into  building  con- 
struction there  occurs  a  sharp  resonance  within  a  not  great  range  of 
pitch.  It  is,  therefore,  necessary  to  determine  the  reverberation  even 
for  the  speaking  voice,  not  for  a  single  pitch  but  for  a  considerable 
range,  and  the  quality  of  a  theatre  with  respect  to  reverberation  will 
be  represented  by  a  curve  in  which  the  reverberation  is  plotted 
against  the  pitch. 

Without  undertaking  to  give  again  a  complete  discussion  of  the 
theorj'  of  reverberation,  and  referring  the  reader  to  the  earlier  (1900) 
numbers  of  The  American  Architect,  it  will  suffice  to  give  a  single 


rnaao-QDDQmD 


ti^ 


3C3 


TT-r; 


Fl09.  7  an<i  8.    Plan  ami  Sct-liim  of  tin-  LillK-  Tlifulir.  NVw  York. 
IiiftalU  uikI  IhitTinuii.  Aixliititls. 


174  THEATRE  ACOUSTICS 

illustration.  For  this  I  have  selected  Mr.  Wintlirop  Ames'  "Little 
'J'heatre"  in  New  York,  designed  by  Messrs.  Ingalls  and  Hoffman, 
because  the  purpose  and  use  of  this  auditorium  was  defined  from  the 
beginning  with  unusual  precision.  The  purpose  was  the  production 
of  plays  which  could  be  adequately  rendered  only  by  the  most  deli- 
cate shades  of  expression,  which  would  be  lost  in  considerable  meas- 
ure if  the  conditions  were  such  as  to  necessitate  exaggeration  of 
feature  or  of  voice.  The  definition  of  its  use  was  that  it  should  seat 
just  less  than  300,  and  that  all  the  seats  were  to  be  as  nearly  as 
possible  of  equal  excellence,  with  the  important  assurance  that  every 
seat  would  be  occupied  at  every  performance. 

The  final  plan  and  section  of  the  Little  Theatre  are  shown  in 
Figs.  7  and  8.  The  initial  pencil  sketch  was  of  an  auditorium  differ- 
ing in  many  architectural  details,  acoustical  considerations  sharing 
in,  but  by  no  means  alone  dictating,  the  steps  leading  to  the  final 
solution  of  the  problem.  The  first  calculations,  based  on  the  general 
lines  of  the  initial  sketch,  and  assuming  probable  materials  and  plaus- 
ible details  of  construction  (plaster  on  tile  walls,  plaster  on  wire  lath 
ceiling,  solid  plaster  cornices  and  moulding),  gave  a  reverberation  as 
shown  in  Curve  1  in  Fig.  9.  This  would  not  have  been  in  excess  of 
that  in  many  theatres  whose  acoustical  qualities  are  not  especially 
questioned.  But  the  luiusual  requirements  of  the  plays  to  be  pre- 
sented in  this  theatre,  and  the  tendency  of  the  public  to  criticize 
whatever  is  unconventional  in  design,  led  both  ]\Ir.  Ames  and  the 
architects  to  insist  on  exceptional  quality.  The  floor  was,  therefore, 
lowered  at  the  front,  the  ceiling  was  lowered,  and  the  walls  near  the 
stage  brought  in  and  reduced  in  curvature,  with,  of  course,  corre- 
sponding changes  in  the  architectural  treatment.  The  rear  wall, 
following  the  line  of  the  rear  seats,  remained  unchanged  in  curvature. 
The  side  walls  near  the  stage  were  curved.  The  net  effect  of  these 
changes  was  to  give  an  auditorium  28  feet  high  in  front,  23  feet  high 
at  the  rear,  48  feet  long  and  49  feet  broad,  with  a  stage  opening  18 
by  31,  and  having  a  reverberation  as  shown  by  Curve  2.  In  order  to 
reduce  still  further  the  reverberation,  as  well  as  to  break  acoustically 
the  curvature  of  the  side  and  rear  walls,  "acoustic  felt"  was  applied 
in  panels.  There  were  three  panels,  6  feet  by  13  feet,  on  each  of  the 
side  walls,  and  seven  panels,  two  4  feet  5  inches  by  13  feet,  two  5 


THEATRK  A(  OT'STICS 


r 


feet  by  10  feet,  two  2  feet  hy  4  iVil,  and  one  8  feet  by  7  feet,  on  the 
rear  wall.  The  resulting  reverberation  is  shown  bj  Curve  3  in  the 
diafjrain.  Throughout,  consideration  was  had  for  the  actual  path  of 
the  sound  in  its  successive  reflections,  but  the  discussion  of  tliis 


8 

8 
7 
6 
5 
4 
3 

1^ 

\ 

\   \     ^ 

v^--^ 

.^ 

] 

2 

\. 

1 

'  2 

~3 

^- 

-^ 

o, 


c, 


c. 


c, 


c. 


c, 


Kio.  !>.  Hovfrlirriilioii  in  sounds  of  llie  Liltlr  Tlicatrr. 
for  iioU-s of  (liirtTi-iil  |)il<li.(']  Iwiiif;  MiililleC,  Curve  I 
f(ir  llir  lirst  <l<slt;M,  Curve  i  for  the  seoiml.nnil  Curve 
;l  for  llie  tliiril  and  as  liulll. 


jiliasi'  of  (lie  gi-neial  i)i()l)lcni  conu-.s  in  llie  next  sctlion  and  will  be 
illustrated  by  otlier  tluatres. 

It  should  be  said.  ])jiniiliirli(ally  Iml  none  llic  less  cMiplialieally, 
that  throughout  this  iKipcr  l>y  Iheatif  i>  nuaiit  an  auditorium  for 
tli('s])ok('n  dranni. 


17(i  THEATRE  ACOUSTICS 


Echo 


When  a  source  of  sound  is  maintained  constant  for  a  sufficiently 
\ouii  time  —  a  few  seconds  will  ordinarily  suffice  —  the  sound  be- 
comes steady  at  every  point  in  the  room.  The  distribution  of  the 
intensity  of  sound  under  these  conditions  is  called  the  interference 


Vie.  l(t.    Interior,  the  New  Theatre,  New  York.     Carrere  and  Hastings,  Architects. 

system,  for  that  particular  note,  of  the  room  or  space  in  question. 
If  the  source  of  sound  is  suddenly  stopped,  it  requires  some  time  for 
the  sovuid  in  the  room  to  be  absorbed.  This  prolongation  of  sound 
after  the  source  has  ceased  is  called  reverberation.  If  the  source  of 
sound,  instead  of  being  maintained,  is  short  and  sharp,  it  travels  as 
a  discrete  wave  or  group  of  waves  about  the  room,  reflected  from 
wall  to  wall,  producing  echoes.   In  the  Greek  theatre  there  was  ordi- 


THEATRE  ACOUSTICS 


r 


narily  hul  one  echo,  "doubling  the  case  ending,"  while  in  the  modern 
theatre  there  are  many,  generally  arriving  at  a  less  interval  of  time 
after  the  direct  sound  and  therefore  less  distinguishable,  but  stronger 
and  therefore  more  disturbing. 

This  pliase  of  the  acoustical  jiroblem  will  be  illustrated  by  two 
examples,  the  New  Theatre,  the  most  important  structure  of  the 


Vw..  II 


kind  in  New  York,  and  the  plans  of  the  theatre  now  building  for  the 
Scollay  Square  Realty  Company  in  Boston. 

Notwithstanding  the  fad  that  there  was  at  one  time  criticism  of 
the  acoustical  (|uaiity  of  the  New  'J'heatre,  the  memory  of  which 
still  lingers  and  slill  colors  the  casual  coininent,  it  was  not  worse  in 
proportion  to  its  size  than  several  ollur  theatres  in  the  city.  It  is, 
therefore,  not  taken  as  an  example  because  it  showed  acoustical  de- 
fects in  reniarkal)if  degree.  l)nl  rather  Ix-canse  there  is  much  that 
can  be  learned  from  the  conditions  under  whidi  it  was  i)uill,  i>ecau.se 
such  defects  as  existed  have  been  corrected  in  large  measure,  and 


178 


THEATRE  ACOI STICS 


above  all  in  the  liojie  of  aiding  in  some  small  way  in  the  restoration 
of  a  magnificent  l)uiUling  to  a  dignified  use  for  which  it  is  in  so  many 
ways  eminently  suited.  The  generous  purpose  of  its  Founders,  the 
high  ideals  of  its  manager  in  regard  to  the  plays  to  be  produced,  and 
the  jierfection  otherwise  of  the  building  directed  an  exaggerated  and 
morbid  attention  to  this  feature.  Aside  from  the  close  scrutiny  which 


Fig.  12 


always  centers  on  a  semi-public  undertaking,  the  architects,  Messrs. 
Carrere  and  Hastings,  suffered  from  that  which  probably  every  archi- 
tect can  appreciate  from  some  similar  experience  of  his  own,  —  an 
impossible  program.  They  were  called  on  to  make  a  large  "little 
theatre,"  as  a  particular  type  of  institution  is  called  in  England;  and, 
through  a  division  of  purpose  on  the  part  of  the  Founders  and  Ad- 
visers, for  the  Director  of  the  Metropolitan  Opera  was  a  powerful 
factor,  they  were  called  on  to  make  a  building  adapted  to  both  the 
opera  and  the  drama.  There  were  also  financial  difficulties,  although 
very  different  from  those  usually  encountered,  a  plethora  of  riches. 
This  necessitated  the  provision  of  two  rows  of  boxes,  forty-eight 
originally,  equally  commodious,  and  none  so  near  the  stage  as  to 


THEATRE  ACOUSTICS 


179 


thereby  suffer  in  coniparisoii  with  the  others.  Finally,  there  was  a 
change  of  program  when  the  building  was  almost  complete.  The 
upper  row  of  boxes  was  abandoned  and  the  shallow  balcony  thus 
created  was  devoted   to  Unrr  chairs  wliich  were  reserved  for  the 


■TW  NlwmtATlt 


Ki(i.  l.'i.   I'laiis  aiul  Section  of  llu-  Now  Tlioalre,  New  York. 
Carr^re  and  Mostings,  Architects. 

annual  subscribers.   As  will  l>c  sIkiwu  later  these  .seats  were  acousti- 
cally the  i)oorest  in  the  !inu>e. 

Encircling  boxes  are  a  familiar  arrangement,  but  most  of  the 
precedents,  especially  those  in  good  repute,  are  oi)era  houses  and 
not  theatres,  the  oj)era  and  tiie  drama  being  ilitVcrent  in  tlieir  acous- 
tical requirenunts.  In  the  New  Theatre  this  arrangement  exertetl  a 
three-fold  pressure  on  the  design.  It  raised  the  l)aleony  and  gallery  ^^2 
feet.  It  increased  both  the  breadth  and  tluMlei)th  of  the  house.  And. 
together  with  the  re(|uirement   that  the.se  boxes  shoidd  not  extend 


180  THEATRE  ACOUSTICS 

near  the  stage,  it  led  to  side  walls  whose  most  uatiual  architectural 
treatment  was  such  as  to  create  sources  of  not  inconsiderable  echo. 
The  immediate  problem  is  the  discussion  of  the  reflections  from 
the  ceiling,  from  the  side  walls  near  the  stage,  from  the  screen  and 
parapet  in  front  of  the  first  row  of  boxes  and  from  the  wall  at  the 
rear  of  these  boxes.  To  illustrate  this  I  have  taken  photographs  of 
the  actual  sound  and  its  echoes  passing  through  a  model  of  the 


Fig.  li.  Photograph  of  a  sound-wave,  (I'll',  entering  a  model 
of  the  New  Theatre,  and  of  the  echoes  Oi,  produced  by  the 
orchestra  screen,  02  from  tlie  main  floor,  (13,  from  the  floor 
of  the  orchestra  pit,  a<,  the  reflection  from  the  orchestra 
screen  of  the  wave  03,  n^  the  wave  originating  at  the  edge  of 
the  stage. 

theatre  by  a  modification  of  what  may  be  called  the  Toeppler-Boys- 
Foley  method  of  photographing  air  disturbances.  The  details  of  the 
adaptation  of  the  method  to  the  present  investigation  will  be  ex- 
plained in  another  paper.  It  is  sufficient  here  to  say  that  the  method 
consists  essentially  of  taking  off  the  sides  of  the  model,  and,  as  the 
sound  is  passing  through  it,  illuminating  it  instantaneously  by  the 
light  from  a  very  fine  and  somewhat  distant  electric  spark.  After 
passing  through  the  model  the  light  falls  on  a  i)hotographic  plate 
placed  at  a  little  distance  on  the  other  side.  The  light  is  refracted  by 
the  soimd-wa\'es,  which  thus  act  practically  as  their  own  lens  in  pro- 
ducing the  photograph. 

In  the  accompanying  illustrations  reduced  from  the  photographs 
the  enframing  silhouettes  are  shadows  cast  by  the  model,  and  all 


Fio.  15 


Fig.  1H 


ii; 


Fig.  19 


In..  IT 


I'lu.  iO 


Two  scries  of  pholnjjrnplis  of  the  soiiml  ami  its  rt-fliTlions  in  llir  Nrw  Tlirnlrr.  —  15  lo  17  licfoir,  IK  to  ill  oflrr 
llu*  installiitinii  (if  tin-  rnnopy  in  thrrt-ilinjj.  'I'lic  rffit-l  of  Ihr  (-iinopy  in  pnttit-tinjj  ihi*  l»ftliMn\'.  foyer  rhnir^, 
boxes,  nnil  the  iirrluvilra  chairs  Imck  »f  row  L  is  shuuii  l>y  coniparinK  Fi^s.  I!)  nnil  -Ht  with  Fifts.  10  Ami  17. 


Ks>  THEATRE  ACOUSTICS 

within  art'  direct  photographs  of  the  actual  sound-wave  and  its 
echoes.  For  examj)le,  Fig.  14  shows  in  silhouette  the  principal  longi- 
tudinal section  of  the  main  auditorium  of  the  New  Theatre.  WW  is 
a  photograph  of  a  sound-wave  which  has  entered  the  main  auditorium 
from  a  jioint  on  tlie  stage  at  an  ordinary  distance  l)ack  of  the  pros- 
cenium arch;  ch,  is  tiie  reflection  from  the  solid  rail  in  front  of  the 
orchestra  pit,  and  Oj,  the  reflection  from  the  floor  of  the  sound  which 
has  passed  over  the  top  of  the  rail;  03  is  the  reflection  from  the  floor 


Fig.  i].  I'liotoKraph  of  the  direct  sound,  WJV,  and  of  the 
echoes  from  the  various  surfaces;  00,3,  a  wave,  or  echo,  due 
to  the  combination  of  two  waves  which  originated  at  the 
orchestra  pit;  ci  from  the  oval  panel  in  the  ccihng;  c^  and 
Cs.  from  the  ceiling  mouldings  and  cornice  over  the  prosce- 
nium arch;  Ci,  a  group  from  the  moulding  surrounding  the 
panel;  Cj,  from  the  proscenium  arch;  ij,  fcj,  he  from  the 
screens  in  front,  and  the  walls  in  the  rear  of  the  boxes, 
balcony  and  gallery. 

of  the  pit,  and  04  the  reflection  of  this  reflected  wave  from  the  rail ; 
while  «5  originated  at  the  edge  of  the  stage.  None  of  these  reflections 
are  important  factors  in  determining  the  acoustical  quality  of  the 
theatre,  but  the  photograph  affords  excellent  opportunity  for  show- 
ing the  manner  in  which  reflections  are  formed,  and  to  introduce  the 
series  of  more  significant  photographs  on  page  181. 

Figures  15,  16,  and  17  show  the  advance  of  the  sound  through  the 
auditorium  at  .07,  .10,  and  .14  second  intervals  after  its  departure 


THEATRE  ACOUSTICS  183 

from  the  source.  In  Fig.  15,  the  waves  wliicli  originated  at  the 
orchestra  ])it  can  be  readily  distinguished,  as  well  as  the  nascent 
waves  where  the  i)riinary  sound  is  striking  the  ceiling  cornice  imme- 
diately over  the  prosceniiun  arch.  The  proscenium  ardi  itself  was 
very  well  designed,  for  the  sound  passed  i)arallel  to  its  surface. 
Otherwise  reflections  from  the  proscenium  arch  wouUl  also  have 
shown  in  the  photograj)!!.  These  would  lia\ c  heen  directed  toward 
tlie  audience  and  miglit  have  heen  very  perceptible  factors  in  deter- 
mining the  ultinuite  acoustical  quality. 

The  system  of  reflected  waves  in  the  succeeding  photograph  in 
the  series  is  so  complicated  that  it  is  difficult  to  identify  the  several 
reflections  by  verbal  descrijjtion.  The  i)hotogra])h  is,  therefore,  re- 
produced in  Fig.  '■21,  lettered  and  with  accompanying  legends.  It  is 
interesting  to  observe  that  all  the  reflected  waves  which  originated 
at  tlie  orchestra  pit  have  disappeared  with  the  exception  of  waves 
Uo  and  a.i.  These  have  combined  to  form  practically  a  single  wave. 
Even  this  combined  wave  is  almost  negligible. 

The  acoustically  important  reflections  in  the  vertical  section  are 
the  waves  Ci,  c^,  and  c^.  The  waves  6i  and  b^  from  the  screen  in  front 
of  the  boxes  and  from  the  back  of  the  boxes  are  also  of  great  impor- 
tance, but  the  peculiarities  of  these  waves  are  better  shown  by  photo- 
graphs taken  vertically  through  a  horizontal  .section. 

The  waves  Ci,  Co,  Ca,  and  bi  and  bo  show  in  a  striking  maniuT  the 
fallacy  of  tlie  not  uncommon  representation  of  the  propagation  of 
sound  by  straight  lines.  For  example,  the  wave  Ci  is  a  reflection  from 
the  oval  j)anel  in  the  ceiling.  The  curvature  of  this  ])anel  is  such 
that  the  ray  construction  would  give  i)ractically  parallel  rays  after 
reflection.  Were  the  geometrical  representation  by  rays  an  ade- 
quate one  the  reflected  \\  ave  would  thus  be  a  flat  disc  e<iual  in  area 
to  the  oblique  projection  of  the  ])anel.  As  a  matter  of  fact,  however, 
the  wave  sjjreads  far  intcj  the  geometrical  shallow,  as  is  shown  by 
the  curved  i)ortion  reaching  well  out  toward  the  proscenium  arch. 
Again,  waves  r„  and  Ci  are  ri-fleclions  from  a  cornice  whose  irregular- 
ities are  not  so  oriented  as  to  suggest  by  the  simple  geometrical 
representation  of  rays  the  formation  of  sucli  waves  as  are  here  clearly 
shown.  Hut  each  >mall  cornice  moulding  originates  an  alnu).sl  hemi- 
spherical wave,  and  llie  mouldings  are  in  two  grou|)s,  the  ])osition  of 


184  THEATRE  ACOUSTICS 

each  being  such  tliat  the  spherical  waves  conspire  to  form  these  two 
master  waves.  The  inadeciuacy  of  the  discussion  of  the  subject  of 
architectural  acoustics  by  the  construction  of  straight  lines  is  still 
further  shown  by  the  waves  reflected  from  the  screens  in  front  of  the 
boxes,  of  the  balcony,  and  of  the  gallery.  These  reflecting  surfaces 
are  narrow,  but  give,  as  is  clearly  seen  in  the  photograph,  highly 
divergent  waves.  This  spreading  of  the  wave  beyond  the  geometrical 
projection  is  more  pronounced  the  smaller  the  opening  or  the  reflect- 
ing obstacle  and  the  greater  the  length  of  the  wave.  The  phenom- 
enon is  called  diffraction  and  is,  of  course,  one  of  the  well-known 
phenomena  of  physics.  It  is  more  pronounced  in  the  long  waves  of 
sound  than  in  the  short  waves  of  light,  and  on  the  small  areas  of  an 
auditoriimi  than  in  the  large  dimensions  of  out-of-door  space.  It 
cannot  be  ignored,  as  it  has  been  heretofore  ignored  in  all  discussion 
of  this  phase  of  the  problem  of  architectural  acoustics,  with  im- 
punity. The  method  of  rays,  although  a  fairly  correct  approximation 
with  large  areas,  is  misleading  under  most  conditions.  For  example, 
in  the  present  case  it  would  have  predicted  almost  perfect  acoustics 
in  the  boxes  and  on  the  main  floor. 

Figures  17  and  20  show  the  condition  in  the  room  when  the  main 
sound-wave  has  reached  the  last  seat  in  the  top  gallery.  The  wave 
Ci  has  advanced  and  is  reaching  the  front  row  of  seats  in  the  gallery, 
producing  the  effect  of  an  echo.  Alittle  later  it  will  enter  the  balcony, 
producing  there  an  echo  greater  in  intensity,  more  delayed,  and 
affecting  more  than  half  the  seats  in  the  balcony,  for  it  will  curve 
under  the  gallery,  in  the  manner  just  explained,  and  disturb  seats 
which  geometrically  would  be  protected.  Still  later  it  will  enter  the 
foyer  seats  and  the  boxes.  But  the  main  disturbance  in  these  seats 
and  the  boxes,  as  is  well  shown  by  the  photograph,  arises  from  the 
wave  Ci,  and  in  the  orchestra  seats  on  the  floor  from  the  wave  Cz. 

In  the  summer  following  the  opening  of  the  theatre,  a  canopy, 
oval  in  plan  and  slightly  larger  than  the  ceiling  oval,  was  hung  from 
the  ceiling  surrounding  a  central  chandelier.  The  effect  of  this  in 
preventing  these  disturbing  reflections  is  shown  by  a  comparison, 
pair  by  pair,  of  the  two  series  of  photographs,  Figs.  15  to  17  and 
Figs.  18  to  20.  It  is  safe  to  say  that  there  are  few,  possibly  no 
modern  theatres,  or  opera  houses,  equal  in  size  and  seating  capacity, 


I'll;    ii  Fio.  ii 

on 

Fio.  <a  t  Hi-  >!•* 

an 

lie,  n  1 1...  it: 

Pliotof^a|>lis  slinwiiiK  ll'c  rfflwlimm.  in  ii  viTti<-al  plane,  from  tlic  siilca  of  ihc  prusiTiiium 
anil,  till-  iiluiii  Willi  lirliiw  llir  iirtnrs'  Imix.  iiiiil  llir  rail  or  scrrrn  in  front  of  the  Uixrs. 
Tlio  |ilioto(;ni|ili»  takni  in  nniiu'riial  sitnirnn-  allow  tin-  (ironrrss  of  n  single  mmuil-wavc 
and  it.t  ri'llotions. 


18C  THEATRE  ACOUSTICS 

whicli  arc  so  free  from  this  parlicular  type  of  disturbance  as  the  New 
Theatre  at  the  present  time. 

In  the  study  of  the  New  Theatre,  photographs  were  taken  through 
several  horizontal  sections.  It  will  l)e  sufficient  for  the  purposes  of 
the  present  jjaper  to  illustrate  the  effect  of  curved  surfaces  in  pro- 
ducing converging  waves  by  a  few  photograjjhs  showing  the  propa- 
gation of  sound  through  a  single  section  in  a  plane  passing  through 
the  parapet  in  front  of  the  boxes.    The  reflected  waves  shown  in 


Fig.  'is.  A  photograpli.  one  uf  luanv  takon,  showing 
in  vertical  section  one  stage  of  tlie  reflection  621 
Fig.  21.  These  reflections  were  eliminated  by  the 
arcliilects  in  the  summer  following  the  opening 
of  the  theatre,  but  have  been  in  part  restored  by 
subsequent  changes. 

Fig.  22  originating  from  the  edge  of  the  proscenium  arch  and  from 
the  base  of  the  column  can  be  followed  throughout  all  the  succeeding 
photographs.  In  Fig.  23  are  shown  waves  originating  from  the  plain 
wall  beneath  the  actor's  box  and  the  beginning  of  some  small  waves 
from  the  curved  parapet.  It  is  easily  possible,  as  it  is  also  interesting 
and  instructive,  to  follow  these  waves  through  the  succeeding  photo- 
graphs. In  Fig.  25  the  sound  has  been  reflected  from  the  rear  of  the 
parajict;  while  in  Fig.  26  it  has  advanced  further  down  the  main 
floor  of  the  auditorium,  narrowing  as  it  proceeds  and  gaining  in  in- 
tensity. The  waves  reflected  from  the  parapet  outside  of  the  aisles 
are  here  shown  approaching  each  other  behind  the  wave  which  has 
been  reflected  from  the  parapet  between  the  aisles.  Waves  are  also 
shown  in  Fig.  26  emerging  from  the  passages  between  the  boxes. 


THKATRE  ACOI'STICS  187 

Indeed,  it  is  possible  to  trace  the  waves  arising  from  a  second  reflec- 
tion from  tlie  proscenium  arch  of  the  sound  wliich,  first  reflected 
from  the  corresponding  surfaces  on  the  other  side,  has  crossed  di- 
rectly in  front  of  the  stage.  With  ;i  lilll<-  care,  it  is  possible  also  to 
identify  tliese  waves  in  tlie  last  ])h()t(ij,'r:i])h. 

Altliough  many  were  taken,  it  will  sufhci-  to  sliow  a  single  jjlioto- 
graph.  Fig.  28,  of  the  reflections  in  the  jilane  passing  through  the 
back  of  the  boxes.  These  disturbing  reflections  were  almost  entirely 
eliminated  in  the  revision  of  the  theatre  by  the  removal  of  the  boxes 
from  the  first  to  the  second  row  and  by  utilizing  the  s])ace  vacated 
logetlier  with  the  anterooms  as  a  single  l)alcony  filled  witli  seats. 

An  excellent  illiLstration  of  tiie  use  of  such  photograjjhs  in  plan- 
ning, before  construction  and  while  all  the  forms  are  still  fluid,  is  to 
l)e  found  in  one  of  the  tlieatres  now  ixMUg  built  in  Boston  by  Mr. 
C.  II.  Blackall,  who  has  had  an  excei)tionally  large  and  successful 
experience  in  theatre  design.  The  initial  pencil  sketch.  Fig.  29,  gave 
in  the  model  test  the  waves  shown  in  the  progressive  series  of  photo- 
graphs. Figs.  .'51  to  fi^.  The  ceiling  of  interix-netrating  cylinders  was 
then  changed  to  the  form  shown  in  finished  section  in  Fig.  :>(•,  with 
the  residts  strikingly  indicated  in  the  i)arallel  series  of  photographs, 
Figs.  34  to  36.  It  is,  of  course,  easy  to  identify  all  tiie  reflections  in 
each  of  the.se  photographs,  —  the  reflections  from  the  ceiling  aiul  tlie 
balcony  front  in  the  first ;  front  the  ceiling  and  from  both  the  balcony 
and  gallery  front  in  the  secoiul;  and  in  the  third  ])li()t<)graph  of  the 
series,  the  reflections  of  the  ceiling  reflection  fmm  ll\e  balcony  and 
gallery  fronts  and  Iroiii  I  Ik  floor.  I?ul  the  es.sential  point  to  be  ob- 
served, in  coinjiaring  the  two  series  ])air  by  pair,  is  the  almost  total 
ab.sence  in  the  second  .series  of  the  ceiling  echo  and  the  nlativcly 
clear  condition  back  of  the  advancing  sound-wave. 

CONSOXANCK 

Con.sonance  is  the  process  whereby,  due  to  >uital>ly  i)laced  rtllect- 
ing  walls,  "(he  voice  is  sui)iiorled  and  >trenglheiu'«l."  It  is  the  one 
acoustical  virtue  liiat  is  |iositive.  It  i^  al-o  tin-  characlerislic  virtue 
of  the  nuxlern  theatre,  and  that  througii  which  this  complicate*! 
auditoriinn  suruKumts  the  at  Iriidant  evils  of  interference,  reverbi-ra- 
lion.  and  echo.    Yet  such  i>  our  nnxlrrn  analv  si>  of  the  prol)Uui  tluit 


188 


THEATRE  ACOUSTICS 


\vc  cU)  not  t'vt-n  havi-  for  it  a  nanu-.  On  the  other  liand.  it  is  the  virtue 
which  tlie  Clreek  theatre  has  in  least  degree.  It  is,  therefore,  all  the 
more  interesting  that  it  should  have  been  included  in  the  analysis  of 
Vitruvius,  and  should  have  received  a  name  so  accurately  descriptive. 
Indeed,  one  can  hardly  make  exjilanation  of  the  phenomenon  better 
than  through  the  very  type  of  theatre  in  which  its  lack  is  the  one 
admitted  defect. 

The  Greek  theatre  enjoys  a  not  wholly  well-founded  reputation 
for  extremely  good  acoustics.    In  most  respects  it  is  deserved;  but 


Fig.  29.    Section  in  pencil  sketcli  of  Scollay  Square  Theatre,  Boston. 
Mr.  C.  H.  Blackall,  Architect. 

the  careful  classical  scholar,  however  gratified  he  may  be  by  this 
praise  of  a  notable  Greek  invention,  regards  himself  as  barred  by 
contemporaneous  evidence  from  accepting  for  the  theatre  imr(uali- 
fied  praise.  E^'ery  traveler  has  heard  of  the  remarkable  quality  of 
these  theatres,  and  makes  a  trial  wherever  opportunity  permits,  be 
it  at  beautiful  Taormina,  in  the  steep  sloped  theatre  at  Pompeii,  the 
great  theatre  at  Ephesus,  or  the  "little  theatre"  on  the  top  of  Tus- 
culum, —  always  with  gratifying  results  and  the  satisfaction  of  hav- 
ing confirmed  a  well-known  fact.  Perhaps  it  is  useless  to  try  to 
traverse  such  a  test.  But  there  is  not  a  theatre  in  Italy  or  Greece 
which  is  not  in  so  ruined  a  condition  today  that  it  in  no  way  what- 
ever resembles  acoustically  its  original  form.    If  its  acoustics  are 


THEATRE  ACOl  STICS 


189 


perfect  today,  they  certainly  were  not  originally.  Complete  "  scaena  " 
and  enclosing  walls  distinctly  altered  the  acoustical  conditions.  The 
traveler  has  in  general  tested  what  is  little  more  than  a  depression 
in  the  ground,  or  a  hollow  in  a  f|uict  country  hillside.  As  a  matter  of 
fact,  the  theatre  in  its  original  form  was  better  than  in  its  ruined 
state.  Still,  witli  all  its  excellencies  it  was  not  wholly  good.  Its 
acoustical  qualities  were  not  wholly  acceptable  to  its  contemporaries. 


Fio.  80.    Finislicil  sirtimi  nf  Stulluy  Sqiiare  Tlieutrt'.  Bosloii.^  Mr.  C.  H.  Blackiill.  .\nliitoct. 

and  would  be  less  acceptable  in  a  mddfiii  tlu-atre,  and  for  modern 
drama. 

Thf  (liflicuitN'  witli  nucIi  casual  evidence  is  that  it  is  gathered 
umlcr  wholly  al>n(>rmal  coiulilions.  Not  only  arc  the  ruins  l)ut  scant 
reminders  of  the  original  structure,  but  the  absence  of  a  large  audi- 
ence vitiates  the  test,  as  it  would  vitiate  a  test  of  any  modern  theatre. 
But  while  in  a  modern  anditoriMin  llie  presence  of  an  audii-nce  almost 
always,  though  not  invariably,  imjjroves  liie  acoustics,  in  the  classical 
theatre  the  presencv  of  an  audience,  in  so  far  us  it  has  any  effect,  is 


190  THKATRE  ACOUSTICS 

disadvantageous.  The  effect  of  an  audience  is  always  twofold,  —  it 
diminishes  the  rever])eration,  and  it  diminishes  the  loudness  or  in- 
tensity of  the  voice.  In  general,  the  one  effect  is  advantageous,  the 
other  disadvantageous.  But  in  the  Greek  theatre,  occupied  or  un- 
occu])ied,  ruined  or  in  its  original  form,  there  was  very  little  rever- 
beration. In  fact,  this  was  its  merit.  On  the  other  hand,  the  very 
fact  that  there  was  little  reverberation  is  significant  that  there  was 
very  slight  architectural  reenforcement  of  the  voice.  One  might  well 
be  unconvinced  l)y  such  a  priori  considerations  were  there  not  ex- 
cellent evidence  that  these  theatres  were  not  wholly  acceptable 
acoustically  even  in  their  day,  and  for  drama  written  for  and  more 
or  less  adapted  to  them.  Excellent  e\'idence  that  there  was  insuffi- 
cient consonance  is  to  be  found  in  the  megaphone  mouthpieces  used 
at  times  in  both  the  tragic  and  the  comic  masks,  and  in  the  proposal 
by  \'itruvius  to  use  resonant  vases  to  strengthen  the  voice. 

The  doubt  is  not  as  to  whether  a  speaker,  turned  directly  toward 
the  audience  and  speaking  in  a  sustained  voice,  could  make  himself 
heard  in  remote  parts  of  a  crowded  Greek  theatre.  It  is  almost  cer- 
tain that  he  could  do  so,  even  in  the  very  large  and  more  nearly  level 
theatres,  such  as  the  one  at  Ephesus.  Better  evidence  of  this  than 
can  be  found  in  the  casual  test  of  a  lonely  ruin  is  the  annual  per- 
formance by  the  staff  of  the  Comedie  Frangaise  in  the  theatre  at 
Orange.  But  even  this,  the  best  preserved  of  either  Greek  or  Roman 
theatres,  is  but  a  ruin,  and  its  temporary  adaptation  for  the  annual 
performance  is  more  modern  than  classical.  A  much  better  test  is  in 
the  exercises  regularly  held  in  the  Greek  Theatre  of  the  University  of 
California,  designed  by  ]Mr.  John  Galen  Howard,  of  which  President 
^^heeler  speaks  in  most  approving  terms.  The  drama,  especially 
modern  drama,  differs  from  sustained  speech  and  formal  address  in 
its  range  of  utterance,  in  modulation,  and  above  all  in  the  require- 
ment that  at  times  it  reaches  the  audience  with  great  dynamic  quality 
but  without  strain  in  enunciation.  Mere  distinctness  is  not  sufficient. 
It  was  through  a  realization  of  this  that  the  megaphone  mouthpiece 
was  invented, — awkward  in  use  and  necessarily  destructive  of  many 
of  the  finer  shades  of  enunciation.  That  it  was  only  occasionally  used 
proves  that  it  was  not  a  wholly  satisfactory  device,  but  does  not  de- 
tract its  evidence  of  weakness  in  the  acoustics  of  the  theatre. 


Via.  'M 


Fig.  S4 


Via.  33 


Fio.  3« 


Two  series  of  plintoKraphs  slmwiDR.  Figs.  31-33.  the  rcfloelions  whicli  would  li«vf  rrsuUeil  from  the  exe- 
riitinn  of  tlio  first  poncil  aki-trli  of  tlic  Scollay  Sqiion-  Tliriitrp  [Vig.  Ht).  and.  Kiss.  M-SO.  from  the 
execution  of  the  second  !ikclch  liy  Mr.  Blacluill  (shown  in  linishol  section  in  V'lg.  30). 


19'^  THEATRE  ACOUSTICS 

The  megaphone  mouthpiece  bears  to  the  acoustics  of  the  Greek 
theatre  tlie  same  evidence,  only  in  a  reciprocal  form,  that  the  mask 
itself  bears  to  the  theatre's  illumination.  It  was  not  possible  to  see 
in  bright  daylight,  particularly  in  the  bright  sunlight  of  the  Mediter- 
ranean atmosphere,  with  anything  like  the  accuracy  and  detail  pos- 
sible in  a  darkened  theatre  with  illuminated  stage.  The  pupil  of  the 
eye  was  contracted,  and  the  sensitiveness  of  the  retina  exhausted  by 
the  brilliancy  of  the  general  glare.  Add  to  this  that  the  distance  from 
the  stage  was  very  much  greater  in  the  Greek  than  in  the  modern 
theatre,  audience  for  audience,  and  one  can  realize  the  reason  for  the 
utter  impossibility  of  facial  expression  in  Greek  dramatization  except 
by  artificial  exaggeration.  The  hea\'iness  and  inflexibility  of  these 
devices,  and,  therefore,  their  significance  as  proof  of  some  inherent 
difficulty  in  dramatic  presentation,  is  emphasized  by  the  delicacy  of 
line  and  fine  appreciation  of  the  human  form  shown  in  other  con- 
temporaneous art. 

Not  less  significant  in  regard  to  the  acoustics  of  the  Greek  theatre 
are  the  directions  given  by  Vitruvius  for  the  reenforcement  of  the 
voice  by  the  use  of  resonant  vases : 

"  Accordingly  bronze  vessels  should  be  made,  proportional  in  size  to  the 
size  of  the  theatre,  and  so  fashioned  that  when  sounded  they  produce  with 
one  another  the  notes  of  the  fourth,  the  fifth,  and  so  on  to  the  double  octave. 
These  vessels  should  be  placed  in  accordance  with  musical  laws  in  niches 
between  the  seats  of  the  theatre  in  such  position  that  they  nowhere  touch 
the  wall,  but  have  a  clear  space  on  all  sides  and  above  them.  They  should 
be  set  upside  down  and  supported  on  the  side  facing  the  stage  by  wedges  not 
less  than  half  a  foot  high.  .  .  .  With  this  arrangement,  the  voice,  spreading 
from  the  stage  as  a  center,  and  striking  against  the  cavities  of  the  different 
vessels,  will  be  increased  in  volume  and  will  wake  an  harmonious  note  in 
unison  with  itself." 

There  is  good  reason  for  believing  that  this  device  was  but  very 
rarely  tried.  This,  and  the  fact  that  it  could  not  possibly  have  ac- 
complished the  purpose  as  outlined  by  Vitruvius,  is  not  germane. 
The  important  point  is  that  its  mere  proposal  is  evidence  that  the 
contemporaries  of  the  Greek  theatres  were  not  wholly  satisfied,  and 
that  the  defect  was  in  lack  of  consonance. 

It  would  be  inappropriately  elaborate  and  beyond  the  possible 
length  of  this  paper  to  give  in  detail  the  method  of  calculating  the 


THEATRE  ACOITSTICS  193 

loudness  of  sound  in  ditJVrful  parts  of  an  auditorium.  That  suhjt-ft 
is  reserved  for  anotlier  paper  in  preparation,  in  which  will  be  given 
not  merely  the  method  of  calculation  but  the  necessary  tables  for  its 
simplification.  It  i.s,  however,  possible  and  proper  to  give  a  general 
statement  of  the  principles  and  processes  involved. 

In  this  discussion  I  shall  leave  out  as  already  adequately  discussed 
the  phenomenon  of  interference,  or  rather  shall  dismiss  the  subject 
with  a  statement  that  when  two  sounds  of  the  same  pitch  are  super- 
posed in  exact  afjreeinent  of  i)liase,  the  intensity  of  the  soimd  is  the 
square  of  tlie  sum  of  the  stjuare  roots  of  their  separate  intensities; 
when  they  are  in  opposite  phases,  it  is  the  square  of  the  difference  of 
the  square  roots  of  their  intensities;  but  when  several  sounds  of  the 
same  j)itch  arrive  at  any  \nnnt  in  the  room  with  a  random  difference 
of  phase  their  probable  intensity  is  the  simple  numerical  sum  of  their 
separate  intensities.  It  is  on  the  assumption  of  a  random  difference 
of  phase  and  an  average  probable  loudness  that  I  shall  here  consider 
the  question.  This  has  the  advantage  of  being  the  simijler  and  also  a 
first  a])i)roximati<)n  in  an  auditorium  designed  for  articulate  si)eech. 

When  sound  spreads  from  a  spherically  symmetrical  source  it 
diminishes  as  the  square  of  the  distance.  When  the  sound  is  being 
projjagated,  still  in  space  unrestricted  by  walls  or  ceiling,  but  over 
the  heads  of  a  closely  seated  audience,  the  law  of  the  dnninution  of 
the  sound  is  more  rapid  than  the  law  of  the  inverse  square.  This  more 
rapid  diminution  of  tiie  sound  is  due  to  the  absorption  of  the  sound 
by  the  audience.  It  is  a  function  of  the  elevation  of  the  speaker  and 
the  angle  of  inclination  of  the  floor,^ — in  other  words,  the  angle  be- 
tween the  sight  lines.  The  diminution  of  the  intensity  of  lii<>  sound 
due  to  distance  is  less  the  greater  this  angle. 

If  the  auditorium  be  enclosed  by  not  too  remote  walls,  the  voice 
coming  directly  from  the  sj)eaker  is  reenforced  by  the  reflection  from 
the  retaining  walls.  However,  it  is  obvious  that  the  sounds  reflected 
from  the  walls  and  ceilings  have  traversed  greater  paths  than  the 
.sound  of  the  voice  which  has  come  directly.  If  this  ditference  of  i)atli 
length  is  great,  the  .sounds  will  not  arrive  simultamx>usly.  If,  i>ow- 
ever,  the  i)ath  differeiurs  are  not  great,  the  reflected  sounds  will 
arrive  in  time  to  reenforce  the  voice  which  has  come  directly,  each 
svllal)le  l)V  itself,  or,  indt-ed,  in  lime  for  the  .self  support  of  the  sub- 


194 


THKATRE  ACOUSTICS 


syllaliic  compoiuMits.  It  is  to  tliis  mutual  strengthening  of  concur- 
rent sounds  within  eacli  ek'nient  of  articulate  speech  that  Vitruvius 
has  given  the  name  "consonance." 

Thus  in  the  computation  of  the  intensity  of  the  voice  which  has 
come  directly  from  the  speaker  across  the  auditorium,  it  is  necessary 
to  take  into  consideration  not  merely  the  duiiiuution  of  intensity 
according  to  the  law  of  the  inverse  square  of  the  distance  and  the 
diminution  of  the  intensity  due  to  the  absorption  by  the  clothing  of 


Fig.  37 


Tlie  Harris  Theatre,  Minneapolis,  first  design. 
Chapman  and  Magnej,  Architects. 


the  audience,  but  also,  as  a  compensating  factor  for  the  latter,  the 
diffraction  of  the  sound  from  above  which  is  ever  supplying  the  loss 
due  to  absorption,  while  in  computing  the  intensity  of  the  sound  re- 
flected from  any  wall  or  other  surface  one  must  take  into  considera- 
tion all  this,  and  also  the  coefficient  of  reflection  of  the  wall  and  the 
diffraction  due  to  the  restrictea  area  of  the  reflecting  element. 

Abstract  principles  are  sometimes  tedious  to  follow  even  when 
not  difficult.  In  Fig.  38  is  shown  a  photograph  taken  in  an  investiga- 
tion for  the  architects,  Messrs.  Chapman  and  Maguey,  of  the  Harris 
Theatre,  to  be  erected  in  Minneapolis,  which  affords  an  excellent 
example  of  both  favorable  and  unfavorable  conditions  in  respect  to 
consonance.    The  initial  sketch  for  this  theatre  offered  no  problems 


THEATRE  ACOUSTICS  19.5 

either  of  interference  or  reverberation,  and  of  echo  only  in  the  hori- 
zontal section.  The  only  very  considerable  question  presented  by  the 
plans  was  in  respect  to  consonance  and  lliere  in  regard  only  to  the 
more  remote  parts  of  the  floor  and  of  tiie  balcony.  'I'lie  particular 
photograph  here  reproduced  records  the  condition  of  the  sound  in 
the  room  at  such  an  instant  as  to  bring  out  this  aspect  of  the  problem 
in  marked  degree. 

The  forward  third  of  the  l)akony  in  this  theatre  affords  an  ex- 
cellent example  of  consonance,  for  the  reflection  from  the  ceiling 
arrives  so  nearly  simultaneously  with  the  sound  which  has  come 


Fig.  38.  Sliow  lug  the  foiisonaiur  In  llu'  bnli-oiiv  df  llic  Harris 
Theatre.  This  relates  only  to  ronsonanre  in  the  vfrtical 
section. 

directly  from  the  stage  as  to  "strengthen  and  sni)porl "  it  and  yet 
"leave  the  words  clear  and  distinct."  The  interval  between  the  two, 
the  direct  and  the  reflected  voice,  varies  from  .01  second  to  .03 
second.  Back  of  the  first  thirtl.  however,  the  consonance  from  the 
ceiling  gradually  diminishes  and  is  practically  imperceptible  beyoiul 
the  middle  of  tin-  galK'iy.  Hack  of  that  i)oint  the  direct  voice  di- 
minishes ra])i<lly  since  it  is  j)assing  in  a  confined  space  over  the  highly 
absorbent  clothing  of  the  audience.  The  loss  of  intensity  at  Uie  rear 
of  the  gallery  is  increased  by  tiie  carrying  of  the  hori/.cntal  portion 
of  the  ceiling  so  far  rearward.  While  the  effect  of  this  is  to  throttle 
the  rear  ol  the  galU-ry  it  obviously  strengthens  the  voice  in  the  for- 
ward third.  Although  there  is  thus  some  compen.sation,  on  the 
whole  the  forward  |)art  of  the  gallery  din-s  not  need  this  service  so 


196  THEATRE  ACOUSTICS 

mucli  as  the  rear  seats.  The  photograph  shows  this  process  clearly: 
the  main  sound-wave  can  be  seen  advancing  after  having  passed  the 
angle  in  the  ceiling.  The  wave  reflected  from  the  ceiling  can  be  seen 
just  striking  the  gallery  seats.  It  is  evident  that  at  the  instant  at 
which  tiic  photograjjli  was  taken  the  sound-wave  was  receiving  the 
last  of  this  sui)port  by  the  sound  reflected  from  the  ceiling. 

The  photograph  also  shows  how  the  sound  after  passing  the  ceil- 
ing angle  spreads  into  the  space  above,  thus  losing  for  the  moment 
thirty  jjor  cent  of  its  intensity,  a  loss,  however,  to  be  regained  in 
considerable  part  later. 

On  the  main  floor  the  reflection  from  the  ceiling  strengthens  the 
direct  voice  only  for  the  long  syllabic  components.  Nevertheless,  in 
comparison  with  other  theatres  the  forward  part  of  the  floor  of  this 
theatre  will  be  excellent.  There  will  be  just  a  trace  of  echo  immedi- 
ately under  the  front  of  the  balcony,  but  this  will  be  imperceptible 
beyond  the  first  four  rows  of  seats  under  the  balcony.  It  is  obvious 
from  the  photograph  that  there  is  no  consonance  in  the  rear  of  the 
main  floor  of  the  auditorium  under  the  balcony. 

A  not  unnatural,  certainly  a  not  uncommon,  inquiry  is  for  some 
statement  of  the  best  height,  the  best  breadth,  and  the  best  depth  for 
a  theatre,  for  a  list  of  commended  and  a  list  of  prohibited  forms  and 
dimensions.  A  little  consideration,  however,  will  show  that  this  is 
neither  a  possible  nor  the  most  desirable  result  of  such  an  inves- 
tigation. 

For  a  simple  rectangular  auditorium  of  determined  horizontal 
dimensions  there  is  a  best  height.  TMien,  however,  the  horizontal 
dimensions  are  changed  the  desirable  height  changes,  although  by  no 
means  proportionally.  When  the  floor  is  inclined,  when  the  walls  are 
curved,  when  there  are  galleries  and  connection  corridors,  when  the 
material  of  construction  is  varied  in  character,  the  problem  becomes 
somewhat  more  intricate,  the  value  of  each  element  being  dependent 
on  the  others.  Moreover  it  is  futile  to  attempt  to  formulate  a  stand- 
ard form  even  of  a  single  tj-pe  of  auditorium.  How  greatly  the 
design  must  vary  is  well  illustrated  in  the  four  theatres  which  have 
been  taken  as  examples,  ^  the  Little  Theatre  with  all  the  seats  on 
the  main  floor,  the  Harris  Theatre,  very  long,  very  broad,  and  with 


THEATRE  ACOUSTICS  197 

but  a  single  gallery,  the  ScoUay  Square  Theatre  with  two  galleries, 
and  the  New  Theatre  with  two  rows  of  boxes  and  two  galleries. 
The  fundamental  conditions  of  the  problem,  not  the  entirely  free 
choice  of  the  architect,  determined  the  general  solution  in  each 
case.  Acoustical  quality  is  never  the  sole  consideration;  at  best  it 
is  but  a  factor,  introduced  sometimes  early,  sometimes  late,  into 
the  design. 


8 
BUILDING  MATERIAL  AND  MUSICAL  PITCH' 

1  HE  iihsorbing  power  of  the  vtirious  materials  that  enter  into 
llic  construction  and  fiirnishinfj  of  an  auditoriinn  is  but  one  phase 
in  the  general  investigation  of  the  subject  of  architectural  acoustics 
which  the  writer  has  been  prosecuting  for  the  past  eighteen  years. 
During  the  first  five  years  the  investigation  was  devoted  almost 
exclusively  to  the  determination  of  the  coefficients  of  absorption 
for  sounds  having  the  i)itch  of  violin  C  (51-2  vibrations  per  second). 
The  results  were  published  in  the  American  Architect  and  the  En- 
gineering Record  in  1900.'  It  was  obvious  from  the  beginning  that 
an  investigation  relating  only  to  a  single  pitch  was  but  a  preliminary 
excursion,  and  that  the  comjjiete  solution  of  the  problem  called  for 
an  extension  of  the  investigation  to  cover  tiie  whole  range  in  pitch 
of  the  sp<Mking  xoice  and  i>l'  I  lie  musical  scalr.  Tlierefore  during 
the  years  wliich  have  since  elapsed  the  investigation  hiis  been  ex- 
tended over  a  range  in  pitch  from  three  octaves  below  to  three 
octaves  above  violin  ('.  That  it  luus  taken  so  long  is  due  to  the  fact 
that  other  aspects  of  the  acoustical  problem  also  pressed  for  solu- 
tion, such  for  example  as  those  depending  on  form,  —  interference, 
resonance,  and  echo.  The  delay  has  also  been  due  in  i)art  to  the 
nature  of  the  investigation,  which  has  necessarily  been  opportunist 
in  character  and.  given  every  opportunity,  somewhat  laborious  and 
exhausting.  Some  meiusure  of  the  labor  involved  may  be  gained 
from  the  fact  that  the  investigation  of  tlir  absorjjlion  coefficients 
for  the  single  note  of  violin  ('  re(|uired  evrry  other  night  from  twelve 
until  livt-  for  a  period  of  three  years. 

While  many  improvements  have  been  made  in  the  inetlioii>  of 
investigation  and  in  IIk'  iipparalns  employed  since  the  first  paper 
was  pul)Iished  fourteen  years  ago.  the  proenl  paper  is  devoted  solely 
to  the  presentation  of  the  re>nll>.  I  shall  venture  to  di.seu.ss,  al- 
though briefly,  the  circmnstances  under  which  the  measurements 

'  Tlic  HrickbuiUlir.  vol.  xxiii,  no.  1,  Jomuiry.  1914.  '  .N".  1.  p   I- 

IN 


200  BUILDING  MATERIAL 

were  inado,  my  ol^ject  heinfj  to  so  interest  architects  that  they  will 
call  attention  to  any  opportunities  which  may  come  to  their  notice 
for  the  further  extension  of  this  work;  for,  while  the  absorbing 
powers  of  many  materials  have  already  been  determined,  it  is 
evident  that  the  list  is  still  incomplete.  For  example,  the  coefficient 
of  glass  has  been  determined  only  for  the  note  first  studied,  C,  an 
octave  above  middle  C.  In  1898  the  University  had  just  com- 
pleted tlie  construction  of  some  greenhouses  in  the  Botanical 
Gardens,  which,  before  the  plants  were  moved  in,  fulfilled  admirably 
the  conditions  necessary  for  accurate  experimenting.  Glass  formed 
a  very  large  part  of  the  area  of  the  enclosing  surfaces,  all,  in  fact, 
except  the  floor,  and  this  was  of  concrete  whose  coefficient  of  absorp- 
tion was  low  and  had  already  been  determined  with  accuracy.  By 
this  good  fortune  it  was  possible  to  determine  the  absorbing  power 
of  single-thickness  glass.  But  at  that  time  the  apparatus  was  adapted 
only  to  the  study  of  one  note;  and  as  the  greenhouse  was  soon  fully 
occupied  with  growing  plants  which  could  not  be  moved  without 
danger,  it  was  no  longer  available  for  the  purpose  when  the  scope 
of  the  investigation  was  extended.  Since  then  no  similar  or  nearly 
so  good  opportunity  has  presented  itself,  and  the  absorbing  power 
of  this  important  structural  surface  over  the  range  of  the  musical 
scale  has  not  as  yet  been  determined.  There  was  what  seemed  for 
the  moment  to  be  an  opportunity  for  obtaining  this  data  in  an  in- 
door tennis  court  which  Messrs.  McKim,  Mead  and  ^Miite  were 
erecting  at  Rhinebeck  on  the  Hudson,  and  the  architects  undertook 
to  secure  the  privilege  of  experimenting  in  the  room,  but  inquiry 
showed  that  the  tennis  court  was  of  turf,  the  absorption  of  which 
was  so  large  and  variable  as  to  prevent  an  accurate  determination 
of  the  coefficients  for  the  glass.  The  necessary  conditions  for  such 
experiments  are  that  the  material  to  be  investigated  shall  be  large 
in  area,  and  that  the  other  materials  shall  be  small  in  area,  low  in 
power  of  absorption,  and  constant  in  character;  while  a  contribut- 
ing factor  to  the  ease  and  accuracy  of  the  investigation  is  that  the 
room  shall  be  so  located  as  to  be  very  quiet  at  some  period  of  the 
day  or  night.  The  present  paper  is,  therefore,  a  report  of  progress 
as  well  as  an  appeal  for  further  opportunities,  and  it  is  hoped  that 
it  will  not  be  out  of  place  at  the  end  of  the  paper  to  point  out  some 


AmsiCAL  PITCH  201 

of  the  problems  which  remain  and  ask  that  interested  architects 
call  attention  to  any  rooms  in  which  it  may  be  possible  to  complete 
the  work. 

The  investigation  does  not  wholly  wait  an  opportunity.  A 
special  room,  exceptionally  well  adapted  to  tlie  i)urpose  in  size, 
shape,  and  location,  h;is  been  constantly  available  for  the  research 
in  one  form  or  another.  This  room,  initially  lined  with  brick  set 
in  cement,  has  been  lined  in  turn  with  tile  of  various  kinds,  with 
plaster,  and  with  plaster  on  wood  lath,  as  well  as  finished  from  time 
to  time  in  other  surfaces.  This  process,  however,  is  expensive,  and 
carried  out  in  completeness  would  be  beyond  what  could  be  borne 
personally.  Moreover,  it  has  further  limitations.  For  example,  it 
is  not  possible  in  this  room  to  determine  the  absorbing  power  of 
glass  windows,  for  one  of  the  essential  features  of  a  window  is  that 
the  outside  space  to  which  the  sound  is  transmit  led  siiall  be  open 
and  unobstructed.  An  inner  lining  of  glass,  even  though  this  be 
placed  several  inches  from  the  wall,  wuul<l  not  with  certainty  repre- 
sent normal  conditions  or  show  tlic  cfrcct  of  windows  as  ordinarily 
employed  in  an  auditorium.  Notwithstanding  these  limitations, 
this  room,  carefully  studied  iti  respect  to  the  effects  of  its  pecu- 
liarities of  form,  especially  such  as  arise  from  interference  and  reso- 
nance, has  been  of  great  service. 

W.\LL   AND    CeILING-SuRF.\CES 

It  is  well  to  bear  in  mind  that  the  absorption  of  sound  by  a  wall- 
surface  is  structural  and  not  superficial.  That  it  is  sujjerficial  is  one 
of  the  most  wi(lcs])rca<l  and  persistent  fallacies.  When  this  investi- 
gation wjui  initially  undertaken  in  an  endeavor  to  correct  the 
acoustics  in  the  lecture-room  of  the  Fogg  .\rt  Mu.seum,  one  of  the 
first  suggestions  was  that  IIh'  walls  wcit  loo  >niootli  and  should  l)e 
roughened.  The  proposal  al  llial  lime  was  that  the  walls  be  re- 
plastered  and  scarred  with  tlir  toothed  trowel  in  a  swirling  motion 
and  then  i)ainted,  a  type  of  deeoraticm  common  twenty  years  ago. 
A  few  years  later  incjuiries  were  received  in  regard  to  sanded  >ur- 
faces,  and  still  later  in  regard  to  a  rough,  pebbly  surface  of  un- 
troweled  plaster;  while  within  the  past  three  years  there  have  been 
many  in(juiries  as  to  the  eilieieney  of  roughened  brick  or  «>f  rough 


i202  BUILDING  MATERIAL 

lu'Wii  stone.  On  tlie  general  principle  of  investigating  any  proposal 
so  long  as  it  conlainetl  even  a  jjossihijity  of  merit,  these  suggestions 
were  put  to  test.  The  concrete  floor  of  a  room  was  covered  with  a 
gravel  so  sifted  that  each  pebble  was  about  one-eighth  of  an  inch 
in  diameter.  This  was  spread  oviT  the  floor  so  that  jx'bhle  touched 
pebble,  making  a  layer  of  but  a  single  pebble  in  thickness.  It 
showed  not  the  slightest  absorbing  power,  and  there  was  no  per- 
ceptible decrease  in  reverberation.  The  room  was  again  tried  with 
sand.  ()f  course,  it  was  not  possible  in  this  case  to  insure  the  thick- 
ness of  a  single  grain  only,  but  as  far  as  possible  this  was  accom- 
plished. The  result  was  the  same.  The  scarred,  the  sanded,  the 
pebbly  plaster,  and  the  rough  hewn  stone  are  only  infinitesimally 
more  efficient  as  absorbents  than  the  same  walls  smooth  or  even 
polished.  The  failure  of  such  roughening  of  the  wall-surfaces  to 
increase  either  the  absorption  or  the  dispersion  of  sound  reflected 
from  it  is  due  to  the  fact  that  the  sound-waves,  even  of  the  highest 
notes,  are  long  in  comparison  with  the  dimensions  of  the  irregu- 
larities thus  introduced. 

The  absorption  of  sound  by  a  wall  is  therefore  a  structural 
phenomenon.  It  is  almost  infinitely  varied  in  the  details  of  its 
mechanism,  but  capable  of  classification  in  a  few  simple  modes. 
The  fundamental  process  common  to  all  is  an  actual  yielding  of  the 
wall-surface  to  the  vibrating  pressure  of  the  sound.  How  much  the 
wall  itields  and  what  becomes  of  the  motion  thus  taken  up,  depends 
on  the  nature  of  the  structure.  The  simplest  type  of  wall  is  obvi- 
ously illustrated  by  concrete  without  steel  reenforcement,  for  in 
this  there  is  the  nearest  approach  to  perfect  homogeneity.  The 
amount  that  this  wall  would  yield  would  depend  upon  its  dimen- 
sions, particularly  its  thickness,  and  upon  the  density,  the  elasticity, 
and  the  viscosity  of  the  material.  It  is  possible  to  calculate  this 
directly  from  the  elements  involved,  but  the  process  would  be 
neither  interesting  nor  convincing  to  an  architect.  It  is  in  every 
way  more  satisfactory  to  determine  the  absorbing  power  by  direct 
experiment.  A  concrete  wall  was  not  available.  In  its  stead,  the 
next  more  homogeneous  wall  was  investigated,  an  eighteen-inch 
wall  of  brick  set  in  cement.  This  wall  was  a  very  powerful  re- 
flector and  its  absorbing  power  exceedingly  slight.     Without  going 


MITSICAL  PITCH  203 

into  Lhc  dt'lails  of  tlu-  cxptiiiiK-nl,  it  will  suffice  here  to  say  that 
this  wall  absorbed  one  and  one-tenth  per  cent  of  the  lowest  note 
investigated,  a  C  two  octaves  below  middle  C,  having  a  vibration 
frequency  of  sixty-four  per  second;  one  and  two-tenths  per  cent 
of  sounds  an  octave  in  pitch  higlur;  one  and  four-tenlhs  per  cent 
of  sounds  of  middle  C;  one  and  seven-tenths  per  cent  for  violin  ("; 
two  per  cent  for  sounds  having  a  pitch  one  octave  above;  two  and 
three-tenths  for  two  octaves  above;  and  two  and  one-half  per  cent 
for  sounds  having  a  pitch  three  octaves  above  violin  C,  that  is  to 
say,  4094  vibrations  per  second,  the  highest  note  investigated. 
These  may  be  WTitten  as  coefficients  of  absorption  thus: 

C,  .011;  Co,  .012;  C3,  .014;   C4,  .017;  C5,  .020;  C,,  .023;  C,,  .025. 

There  is  a  graphical  niclhod  of  presenting  these  results  which  is 
always  employed  in  physics,  and  frequently  in  other  branches  of 
science,  when  the  i)lienomenon  under  investigation  is  simjjly  pro- 
gressive and  dependent   upon  a  single  variable.     Whenever  these 
conditions   are   satisfied  —  and   they   are   usually  satisfied   in   any 
well    conducted     investigation       the    grajjhical    re[)resentation    of 
the  results  takes  the  form  of  a  diagram  in  which  tlie  n-sults  of  the 
measurements   are   plotted    vertically   at    horizontal   distances   de- 
termined by  the  variable  condition.     Thus  in  the  following  diagram 
(Curve  1,  Fig.  1)  the  coi'liicients  of  absorption  are  ])lotted  vertically, 
the  varying  pitch  being  represented  by  horizontal  distances  along  the 
base  line.    Such  a  diagrammatic  representation  serves  to  reveal  the 
accuracy  of  the  work.     If  the  phenomenon   is  a  continuous  one, 
the  plotted  points  should  lie  on  a  smooth  curve;   the  nearness  with 
which  they  do  .so  is  a  measure  of  the  accuracy  of  the  work  if  the 
points  thus  plotted  an-  determined  1>\   tiitircly  independent  experi- 
iiiiiils.     This  form  of  diagranuuatic  representation  serves  another 
piir|)ose  in   i)ermitting  of  the  convenient    interpolation  for  values 
intermediate   between  observed   values.     'I'lie  coeiiicients  f»)r  each 
type  of  wall-surface  will  be  given  i>olh  numerically  and  diagram- 
matically.     In  onlt  r  lo  avoid  confusion,  the  ob-served  points  have 
been  indicated  oidy  on  the  curve  for  wood  sheathing  in  Fig.  1.     It 
will  suffice  to  say  merely  that    the  other  curves  on   this  diagram 
are  drawn  accurately  through  the  plotted  observations. 


^204 


Bl  ILDING  INIATERIAL 


The  next  wall-surface  investigated  was  jilaster  on  hollow  terra 
cot  I  a  tile.  Tlie  plaster  coat  was  of  gjpsuni  hard  plaster,  the  rough 
phuster  being  five-eighths  of  an  inch  in  thickness.  The  result  shows 
a  slightly  greater  absorption  due  to  the  greater  flexibility  of  a  hollow 

10 


c, 


a 


c, 


c 


c„ 


Fig.  1.  Absorbing  power  for  sounds  varying  in  pitch 
from  C  =  6i  to  C  =  4,090;  1,  brick  wall;  2,  plaster 
on  terra  cotta  hollow  tile;  3,  plaster  on  wire  lath; 
4,  same  with  skim  coat;  5,  wood  sheathing. 

tile  wall  rather  than  to  any  direct  effect  of  the  plaster.  The  differ- 
ence, however,  is  not  great.  The  numerical  results  are  as  follows 
(Curve  2,  Fig.  1): 

Ci,  .012;  Ci,  .013;  Cs,  .015;  C4,  .020;   C^,  .028;  Ce,  .040;  C7,  .050. 

Ci  is  the  lowest  note,  64  vibrations  per  second;  C7,  the  highest, 
4,096  per  second;   the  other  notes  at  octave  intervals  between. 


MISICAL  PITCH  205 

Plaster  on  an  otherwise  homogeneous  sustaining  wall  is  a  first 
step  in  the  direction  of  a  compound  wall,  l)ut  a  vastly  greater  step 
is  taken  when  the  plaster  instead  of  being  applied  directly  to  the 
sustaining  wall  is  furred  to  a  greater  or  less  distance.  In  a  homo- 
geneous wall,  the  absorption  of  sound  is  jjartially  by  connnunication 
of  the  vibration  to  the  material  of  the  wall,  whence  it  is  tele|)honed 
throughout  the  structure,  and  partlv  b\-  a  yieliling  of  the  wall  as  a 
whole,  the  sound  bi-ing  then  comnuuiicatcd  to  outside  space.  In 
a  compound  wall  in  which  the  exposed  surface  is  furred  from  the 
main  structure  of  the  wall,  the  former  vibrates  between  the  furring 
strips  like  a  drum.  Such  a  surface  obviously  yields  more  than  woultl 
a  surface  of  plaster  applied  directly  to  tile  or  brick.  The  energy- 
which  is  thus  absorbed  is  partly  dissipated  l)y  the  viscosity  of  the 
plaster,  partly  by  transmission  in  the  air  space  behind  it,  and  partly 
through  the  furring  strips  to  the  main  wall.  The  mechanism  of 
this  process  is  interesting  in  that  it  shows  how  the  free  standing 
plaster  may  absorb  a  great  amount  of  sound  and  may  present  a 
greater  j)ossibility  of  resonance  and  of  selec-tive  absorption  in  the 
different  registers  of  pitch.  It  is  obvious  that  we  are  here  dealing 
with  a  problem  of  more  complicated  aspect.  It  is  conceivable 
that  the  absor|)tion  coefficient  should  dejjend  on  the  naturt>  of  the 
supjjorting  construction,  whether  wood  lath,  wire  lath,  or  expandetl 
metal  lath;  on  the  distance  apart  of  the  studding,  or  the  de|)th  of 
the  air  space;  or,  and  i  \<ii  more  decidedly,  on  the  nature  of  the 
plaster  emi)loyetl,  whether  tiie  old  lime  |)las(er  or  the  modern  ([uick 
setting  gypsum  plaster.  A  start  has  been  made  on  a  stu(l\'  of  this 
problem,  but  it  is  not  as  yet  so  far  ailvanced  as  to  [x-rmit  of  a  system- 
atic correlation  of  the  results.  It  nuist  suffice  to  present  here  the 
values  for  a  single  construction.  The  most  interesting  case  is  that 
in  which  lime  |)laster  Wius  ai)plied  to  wood  lath,  on  wood  studding 
at  fourteen-inch  spacing,  forming  a  two-inch  air  space.  The  co- 
efficients of  al)sorption  before  the  finishing  coat  wsis  put  on  were 
(Curve  3,  Kig.  1): 

Ci,  .048;  Ci.  MO;  C,,  .024;  C4,  .034;  C».  .030;  C«,  .0«8;  Ct.  .043. 

The  values  ;iflrr  the  finishing  coat  was  put  on  were  as  follows 
(Curve  4,  dotted,  I'ig.  1): 

C„  .080;  C„  .OW;   C3.  .OKJ;  C«.  .018;   C.,  .045;  C„  .0^8;   (;,  .0.>5. 


206  BIILDIXG  :MATERIAL 

It  should  he  iTinarkccl  that  the  determination  of  these  coefficients 
was  made  witliin  two  weeks  after  the  plaster  was  applied  and  also 
that  the  modern  lime  is  not  the  same  as  the  lime  used  thirty  years 
ago,  either  in  the  manner  in  which  it  is  handled  or  in  the  manner 
in  which  it  sets  and  dries.  It  is  particularly  interesting  to  note  in 
these  observations,  more  clearly  in  the  plotted  curves,  the  phe- 
nomenon of  resonance  as  shown  by  the  maxima,  and  the  effect  of 
the  increased  thickness  produced  by  the  skim  coat  in  increasing  the 
rigidity  of  the  wall,  decreasing  its  absorbing  power,  and  shifting  the 
resonance. 

The  most  iirmlj^  established  traditions  of  both  instrumental  and 
architectural  acoustics  relate  to  the  use  of  wood  and  excite  the 
liveliest  interest  in  the  effect  of  wood  sheathing  as  an  interior  sur- 
face for  auditoriums;  nor  are  these  expectations  disappointed  when 
the  i)lK'nonK'non  is  submitted  to  exact  measurement.  It  was  not 
easy  to  find  satisfactory  conditions  for  the  experiment,  for  not 
many  rooms  are  now  constructed  in  which  plaster  on  studding,  and 
sufficiently  thin,  forms  a  very  considerable  factor.  After  long  waiting 
a  room  suitable  in  everj-  respect,  except  location,  became  available. 
Its  floor,  its  whole  wall,  indeed,  its  ceiling  was  of  pine  sheath- 
ing. The  only  other  material  entering  into  its  construction  was 
glass  in  the  two  windows  and  in  the  door.  Unfortunately,  the  room 
was  on  a  prominent  street,  and  immediately  adjacent  was  an  all- 
night  lunch  room.  Accurate  experiments  were  out  of  the  question 
while  the  lunch  room  was  in  use,  and  it  was,  therefore,  bought  out 
and  closed  for  a  few  nights.  Even  with  the  freedom  from  noise 
thus  secured,  the  experiments  were  not  totally  undisturbed.  The 
traffic  past  the  building  did  not  stop  sufficiently  to  permit  of  any 
observations  until  after  two  o'clock  in  the  morning,  and  began  again 
by  foiu".  During  the  intervening  two  hours,  it  was  possible  to 
snatch  periods  for  observation,  but  even  these  periods  were  dis- 
turbed through  the  curiosity  of  passers  and  the  more  legitimate 
concern  of  the  police. 

Anticipating  the  phenomenon  of  resonance  in  wood  in  a  more 
marked  degree  than  in  any  other  material,  new  apparatus  was 
designed  permitting  of  measurements  at  more  frequent  intervals 
of  pitch.     The  new  apparatus  was  not  available  when  the  work 


:\n'SICAL  PITCH  ^,'((7 

began  and  the  coefficients  for  the  wood  were  deterniiiicd  ;il  octave 
intervals,  with  resuHs  as  follows: 

Ci,  .064;   Co,  .098;  C,,  .112;  C*,  .104;  C.,  .081;  Ce,  .082;   Ct,  .U.S. 

These  results  when  plotted  .^llowed  clearly  a  very  marked  reso- 
nance. The  more  elaborate  apparatus  was  hastened  to  completion 
and  the  coefficients  of  absorption  determined  for  the  intermediate 
notes  of  E  and  G  in  each  of  the  middle  four  octaves.  The  results  of 
both  sets  of  experiments  when  plotted  together  give  Curve  5  in 
Fig.  1.  The  accuracy  with  which  these  fourteen  jxiints  fall  on  a 
smooth  curve  drawn  through  them  is  all  llial  ((mid  lie  cxjx'cted  in 
view  of  the  conditions  under  which  the  experiment  was  conducted 
and  the  limited  time  available.  Only  one  j)oint  falls  far  from  the 
curve,  that  for  middle  C  (C3,  "250).  The  general  trend  of  the  curve. 
however,  is  e.stablished  beyond  rea.sonable  doubt.  It  is  interesting 
to  note  the  \-erv  great  differenci's  bet\\(<'ii  this  curve  and  tho.se 
obtained  lor  solid  walls,  and  even  for  plastered  walls.  It  is  espe- 
cially interesting  to  note  the  great  absorjjtion  due  to  the  resonance 
between  the  natural  vibration  of  the  walls  and  the  sound,  and  to 
observe  that  this  maximum  i)<)int  of  resonance  lies  in  the  lower  i)art, 
although  not  in  the  lowest  \n\r\,  of  the  range  of  j)itcli  tested.  The 
pitch  of  this  resonance  is  determined  by  the  nature  of  the  wo(kI,  its 
thickness,  and  the  distance  apart  of  the  stutlding  on  which  it  is 
supported.  The  wood  tested  was  North  Carolina  pine,  five-eighths 
of  an  inch  in  thickness  and  on  studding  fourteen  inches  apart.  It 
is,  perhaps,  not  superfluous  to  add  at  this  time  that  a  denser  wood 
woulil  have  had  a  lower  i)itch  for  nuixinunn  resonance,  other  con- 
ditions being  alike;  an  increa.sed  thickness  would  have  raised  the 
|)it(li  of  llie  resouaiice;  while  an  iiierea>ed  distance  betwtHMi  the 
studding  would  have  lowered  it.  I'inally  it  should  be  addetl  that 
the  best  acoustical  condition  both  for  music  and  for  speaking  would 
have  been  with  the  nuiximum  resonance  an  octave  al)ove  rather 
than  at  middle  C. 

Even  more  interesting  is  the  study  of  ceramic  tih-  made  at  the 
ref|uest  of  Messrs.  Cram,  (Joodhue,  and  Ferguson  'Ihe  iiiv«'sliga- 
tion  had  for  its  first  object  the  determination  of  the  acoustical 
value  of  the  tile  as  employed  in  the  grointnl  arches  of  the  Chapel  of 


208  BLTILDING  M.\TERIAL 

tlic  T'liitcd  States  Military  Academy  at  West  Point.  The  investi- 
gation then  widened  its  scope,  and,  through  the  skill  and  great 
knowledge  of  ceramic  processes  of  Mr.  Raphael  Guastavino,  led  to 
really  remarkable  results  in  the  way  of  improved  acoustical  effi- 
ciency. The  resulting  construction  has  not  only  been  approved  by 
architects  as  equal,  if  not  better,  in  architectural  appearance  to 
ordinary  tile  construction,  but  it  is,  so  far  as  the  writer  knows,  the 
first  finished  structural  surface  of  large  acoustical  efficiency.  Its 
random  use  does  not,  of  course,  guarantee  good  acoustical  quality 
in  an  auditorium,  for  that  depends  on  the  amount  used  and  the 
surface  covered. 

The  first  investigation  was  in  regard  to  tile  used  at  West  Point, 
with  the  following  result : 

Ci,  .012;  C2,  .013;  C3,  .018;  C4,  M9;  C„  .040;  Ce,  .048;  C7,  .053. 

These  are  plotted  in  Curve  1,  Fig.  2.  The  first  endeavors  to  im- 
prove the  tile  acoustically  had  very  slight  results,  but  such  as  they 
were  they  were  incorporated  in  the  tile  of  the  ceiling  of  the  First 
Baptist  Church  in  Pittsburgh  (Curve  2,  Fig.  2). 

Ci,  .028;  C2,  .030;  C3,  .038;  C4,  .053;  C5,  .080;  Ce,  .102;  C7,  .114. 

There  was  no  expectation  that  the  results  of  this  would  be  more 
than  a  very  slight  amelioration  of  the  difficulties  which  were  to  be 
expected  in  the  church.  In  consequence  of  its  use,  the  tile  may  be 
distinguished  for  purposes  of  tabulation  as  Pittsburgh  Tile.  With- 
out following  the  intermediate  steps,  it  is  sufficient  to  say  that  the 
experiments  were  continued  nearly  two  years  longer  and  ultimately 
led  to  a  tile  which  for  the  conveniences  of  tabulation  we  will  call 
Acoustical  Tile.  The  resulting  absorbent  power  is  far  beyond  what 
was  conceived  to  be  possible  at  the  beginning  of  the  investigation, 
and  makes  the  construction  in  which  this  tile  is  incorporated  unique 
in  acoustical  value  among  rigid  structures.  The  coefficients  for  this 
construction  are  as  follows: 

Ci,  .064;  C2,  .068;  C3,  .117;  C4,  .188;  C„  .250;  Ce,  .258;  C7,  .223, 

graphically  shown  in  Curve  3,  Fig.  2.  It  is  not  a  panacea.  There 
is,  on  the  other  hand,  no  question  but  that  properly  used  it  will  very 
greatly  ameliorate  the  acoustical  difficulties  when  its  employment 


MUSICAL  PITCH 


209 


is  practicable,  and  used  in  proper  locations  and  amounts  will  render 
the  acoustics  of  many  auditoriums  excellent  which  would  otherwise 
be  intolerable.  It  has  over  sixfold  tlic  ahsorbiiif,'  [)ower  of  any  exist- 
ing masonry  construction  and  oiu'-tliird  tiic  ahsorhing  power  of  the 


10 


^ 

S 

\ 

/ 

\ 

/ 

/ 

4 
/ 

/ 

.X 

f^             ^ 

-\ 

^ 

-^ 

^rr 

:=:= 

'2 

-'' 

— 

' 

c, 


c. 


C,  C,  Cj  c. 

Fig.  i.     Absorbing  power:   1,  West  Point  tile;   2,  Pitls- 

l)iir(;li  tile;  3,  arotisticnl  tile;  \,  best  felt. 

best  known  felt  |)lott((l  on  tlie  same  diagram  for  comparison  (Curve 
4).    It  is  a  new  factor  ;il  I  lie  dis])()sal  of  tlu'  architect. 

ClI.\lH.S    .\N»   AUDIKXCE 

Efiually  itM|)oil;mt  witli  the  \\;ill  ;m<l  eeiling-surfaees  of  an 
auditorium  arc  its  conlcnls,  cspcciidiy  I  lie  scats  and  tlic  audirnec. 

In  Impressing  I  la-  coellii'ienls  of  al>sor|)tion  for  objects  whieh  are 
themselves  units  ami  which  eamiol  be  hgured  lus  areius,  the  coefli- 


210 


BOLDING  :MATERIAL 


cicnts  clci)i'iul  on  iiic  .system  of  measurement  employed,  Metric  or 
English.  While  the  international  or  metric  system  has  become 
universal  except  in  English  speaking  countries,  and  even  in  England 
and  America  in  many  fields,  it  has  not  yet  been  adopted  by  the 


10 

9 

8 

7 

6 

5 

/6- 

4 

/ 

X 

3 

/1 

_^ 

a 

/ 

"M 

s 

\v, 

-J 

■-    \ 

^ 

1 

y     ^^ 

Z=^ 

I , 

-^ 

c, 


c. 


c, 


C,; 


c, 


c,        c, 

Fig.  3.  Absorbing  power:  1,  bent  wood  chairs;  2,  3,  4, 
and  5,  various  kinds  of  pew  cushions  as  described  in 
text;  0,  audience  per  person. 

architectural  profession  and  by  the  building  trades,  and  therefore 
these  coefficients  will  be  given  in  both  systems. 

Ash  settees  or  chairs,  such  as  are  ordinarily  to  be  foimd  in  a 
college  lecture-room,  have  exceedingly  small  absorbing  powers. 
Such  furniture  forms  a  very  small  factor  in  the  acoustics  of  any 
auditorium  in  which  it  is  employed.  The  coeflBcients  for  ash  chairs 
are  as  follows  (Curve  1,  Fig.  3): 


MUSICAL  PITCH  211 

Metric 
C„.014;  C2,  .014;  Cj,  .015;   C4.  .016;  Cj,  .017;  C«.  .019;  C7.  .021. 

Knglitih 
C,  .15;   C,  .15;   C3,  .16;   C^,  .17;   C,,  .18;   Ce,  .20;   C7,  23. 

The  coefficients  for  settees  were  also  determined,  hut  differ  so  little 
from  those  for  chairs  that  this  pajjer  will  not  he  hurdened  with 
them.  When,  however,  the  seats  are  upholstered,  they  immediately 
become  a  considerable  factor  in  the  acoustics  of  an  empty,  or  par- 
tially empty,  auditorium.  Of  course  the  chairs  either  upholstered 
or  unui)liolstered  are  not  a  factor  in  the  acoustics  of  the  auditorium 
when  occupied.  The  absorbing  power  of  cushions  depends  in  con- 
siderable measure  upon  the  nature  of  the  covering  and  upon  the 
nature  of  the  padding.  Tlie  cushions  experinu-nted  ui)on  were  such 
SIS  are  employed  in  church  pews,  hut  the  coifiicients  are  expressed 
in  terms  of  the  cushion  which  would  cover  a  single  seat.  The  co- 
eflBcients  are  as  follows: 

Cushions  of  wiry  vegetal)le  fiber  covered  witli  canvas  and  a  thin 
damask  cloth  (Curve  '■2,  Fig.  .'5): 

Metric 
C,,  .060;  C2,  .070;  C3,  .097;  C4,  .135;  C,,  .148;  C,,  .132;  C7,  .115. 

English 
Ci,  .64;  Cj,  .75;  C,,  1.04;  C4,  1.45;  Cs,  1.59;  Ct,  1.42;  C-,  1.24. 

Cushions  of  long  hair  covered  with  canvas  and  with  an   outer 
covering  of  plusii  (Curve  15,  Fig.  .'5): 

Metric 
C  .080;  C2,  .092;  C3,  .105;  C4,  .165;  C,.  .155;  C,.  .128;  Cj,  .085. 

F.nglinh 
C.  .86;  C5,  .09;  C,,  1.13;   („  1.77;   C,,  1.67;  C»,  1.37;   C7.  .91. 

Cushions  of  hair  covered  with  canvas  and  an  outer  covering  of 
thin  leatherette  (Curve  4,  Fig.  3): 

Metric 
C„.062;   C»,  .105;   Cj.  .118;   C,.  .ISd;   (\,  .IIS;   C,.  .06H;  C,.  .040. 


'2U  BUILDING  MATERIAL 

English 
C„  .67;  Co,  1.13;   C,,  1.27;  C4,  1.93;  C^,  1.27;  Cj,  .73;  C7,  .43. 

Elastic  felt  cushions  of  commerce,  elastic  cotton  covered  with 
canvas  and  a  short  nap  plush  (Curve  5,  Fig.  3) : 

Metric 
Ci,  .092;  Co,  .155;   C3,  .175;   C4,  .190;   Cs,  .258;   Ce,  .182;   C7,  120. 

English 
Ci,  .99;  C2,  1.66;  C3,  1.88;   C4,  2.04;   d,  2.77;   Ce,  1.95;   C7,  1.29. 

Of  all  the  coefficients  of  aV)sorption,  obviously  the  most  diflScult 
to  determine  are  those  for  the  audience  itself.  It  would  not  at  all 
serve  to  experiment  on  single  persons  and  to  assume  that  when  a 
number  are  seated  together,  side  by  side,  and  in  front  of  one  an- 
other, the  absorbing  power  is  the  same.  It  is  necessary  to  make  the 
experiment  on  a  full  audience,  and  to  conduct  such  an  experiment 
recjuires  the  nearly  perfect  silence  of  several  hundred  persons,  the 
least  noise  on  the  part  of  one  vitiating  the  observation.  That  the 
experiment  was  ultimately  successful  beyond  all  expectation  is  due 
to  the  remarkable  silence  maintained  by  a  large  Cambridge  audi- 
ence that  volunteered  itself  for  the  purpose,  not  merely  once,  but 
on  four  separate  occasions.  The  coefficients  of  absorption  thus  de- 
termined lie,  with  but  a  single  exception,  on  a  smooth  curve  (Curve  6, 
Fig.  3).  The  single  exception  was  occasioned  by  the  sound  of  a 
distant  street  car.  Correcting  this  observation  to  the  curve,  the 
coefficients  for  an  audience  per  person  are  as  follows : 

Metric 
Ci,  .160;  C2,  .332;   C3,  .395;  C4,  .440;  C5,  .455;   Ce,  .460;   C7,  .460. 

English 
Ci,  1.72;  C2,  3.56;  C3,  4.25;   C4,  4.72;  Cs,  4.70;  Ce,  4.95;  C7,  4.95. 

Fabrics 

It  is  e\'ident  from  the  above  discussion  that  fabrics  are  high 
absorbents  of  sound.  How  effective  any  particular  fabric  may  be, 
depends  not  merely  on  the  texture  of  its  surface  and  the  material. 


MUSICAL  PITCH 


213 


but  upon  the  weave  or  felting  throughout  its  body,  and  of  course, 
also  upon  its  thickness.  An  illuminating  study  of  this  question 
can  be  made  by  means  of  the  curves  in  Fig.  4.  In  this  figure  are 
plotted  the  coefficients  of  absorption  for  varying  thicknesses  of  felt. 
Curve  1  is  the  absorption  curve  for  felt  of  on<'-lialf  iiuh  thickness. 

10 


,^ 

^ 

k 

1^ 

^^ 

// 

f 



V 

/ / 

// 

1 

1 

r 

^y 

// 

/ 

1 

/ 

/ 

/ 

^ 

y 

/ 

— - 

-^ 

^ 

c, 


c. 


c. 


c. 


c, 


Kici.  4.  Absorbing  power  of  felt  of  varying  thirkm-sji.  from 
oiii'-lmlf  to  llirce  iiiclii-s.  showing  by  exlni|M>lnlii)ii  llie 
nbsoriilion  l>y  lliiii  fabrics  of  tbr  ii|>|iir  nxi^'i'r  only. 

Curve  2  of  fell  of  one  incli  thickness,  anil  so  on  up  to  Curve  (>,  which 
is  for  felt  of  three  incht-s  in  tiiickness.  It  is  interesting  to  contem- 
plate what  the  result  of  the  process  would  be  were  it  continued  to 
greater  thickness,  or  in  the  o|)|)osite  direction  to  felt  of  less  and  less 
thickness.  It  is  incoii(<'iva])lc  fliat  felt  should  be  ust-d  more  than 
three  inches  in  thickness  and,  therefore,  extrapolation  in  lliis  direc- 


i214  BllLDIXG  ISLVTERIAL 

tion  is  of  academic  interest  only.  On  the  other  hand,  felt  with  de- 
creasing thickness  corresponds  more  and  more  to  ordinary  fabrics. 
If  this  process  were  carried  to  an  extreme,  it  would  show  the  eflfect 
of  cheesecloth  or  hunting  as  a  factor  in  the  acoustics  of  an  audito- 
rium. It  is  obvious  tliat  very  thin  fabrics  absorb  only  the  highest 
notes  and  are  negligible  factors  hi  the  range  of  either  the  speaking 
voice  or  of  music.  On  the  other  hand,  it  is  evident  that  great  thick- 
ness of  felt  absorbs  the  lower  register  without  increasing  whatever 
its  absorption  for  the  upper  register.  Sometimes  it  is  desirable  to 
absorb  the  lower  register,  sometimes  the  upper  register,  but  far  more 
often  it  is  desirable  to  absorb  the  sounds  from  C3  to  Ce,  but  espe- 
cially in  the  octave  between  C4  and  Cg. 

The  felt  used  in  these  experiments  was  of  a  durable  nature  and 
largely  composed  of  jute.  Because  wool  felt  and  ordinary  hair  felt 
are  subject  to  rapid  deterioration  from  moths,  this  jute  felt  was  the 
only  one  which  could  be  recommended  for  the  correction  of  audi- 
toriums until  an  interested  participator  in  these  investigations  de- 
\el()ped  an  especially  prepared  hair  felt,  which  is  less  expensive  than 
jute  felt,  but  which  is  much  more  absorbent.  Its  absorption  curve 
is  plotted  in  Fig.  i. 

Location 

Such  a  discussion  as  this  should  not  close  without  pointing  out 
the  triple  relation  between  pitch,  location,  and  apparent  power  of 
absorption.  This  is  shown  in  Fig.  5.  Curve  1  shows  the  true  co- 
eflBcient  of  absorption  of  an  especially  effective  felt.  Curve  2  is  its 
apparent  absorption  when  placed  in  a  position  which  is  one  of  loud- 
ness for  the  lower  register  and  of  relative  silence  for  the  upper 
register.  Curve  3  is  the  apparent  coefficient  of  absorption  of  the 
same  felt  when  placed  in  a  position  in  the  room  of  maximum  loud- 
ness for  all  registers.  It  is  evident  from  these  three  curves  that  in 
one  position  a  felt  may  lose  thirtj^  per  cent  and  over  of  its  efficiency 
in  the  most  significant  register,  or  may  have  its  cfficiencj'  nearly 
doubled.  These  curves  relate  to  the  efficiency  of  the  felt  in  its  effect 
on  general  reverberation.  Its  efficiency  in  the  reduction  of  a  dis- 
cTete  echo  is  dependent  to  an  even  greater  degree  on  its  location 
than  on  pitch. 


MUSICAL  PITCH 


215 


The  above  are  the  coefficients  of  absorption  for  most  materials 
usually  occurring  in  auditorium  construction,  but  there  are  certain 
omissions  which  it  is  highly  desirable  to  supply,  particularly  notice- 
able among  these  is  the  absorption  curve  for  glass  and  for  old  phister. 


10 


Fio.  5.  Uoulilc  <lo|>riiil<-n<c  iif  iiliwirlpiin!  |ii>«rr  ■•ii  iJiloh 
and  on  liK-ntiiin.  sliouinK  one  of  llir  wmrifs  of  error 
nliii'li  iiiiist  l>r  K'uanli-tl  n»;iiiii!it  in  tlir  ilrtrnnination  of 
riK-iririfnls  of  uli!W>r|ilion  ami  in  llic  n»r  of  nlisoriiing 
iiintcriaU. 


^>1(5  BUILDING  MATERIAL 

It  is  necessary  for  such  experiments  that  rooms  practically  free  from 
furniture  should  be  available  and  that  the  walls  and  ceiling  of  the 
room  should  be  composed  in  a  large  me.asure  of  the  material  to  be 
testetl.  The  author  would  aj)preciate  any  opportunity  to  carry  out 
such  experiments.  The  opportunity  would  ordinarily  occur  in  the 
construction  of  a  new  building  or  in  the  remodeling  of  Jin  old  one. 

It  may  be  not  wholly  out  of  place  to  point  out  another  modern 
acoustical  difficulty  and  to  seek  opportunities  for  securing  the  neces- 
sary data  for  its  solution.  Coincident  with  the  increased  use  of 
reenforced  concrete  construction  and  some  other  building  forms 
there  has  come  increased  complaint  of  the  transmission  of  sound 
from  room  to  room,  cither  through  the  walls  or  through  the  floors. 
Whether  the  present  general  complaint  is  due  to  new  materials  and 
new  methods  of  construction,  or  to  a  greater  sensitiveness  to  un- 
necessary noise,  or  whether  it  is  due  to  greater  sources  of  disturbance, 
heavier  traffic,  heavier  cars  and  wagons,  elevators,  and  elevator 
doors,  where  elevators  were  not  used  before,  —  whatever  the  cause 
of  the  annoyance  there  is  urgent  need  of  its  abatement  in  so  far  as 
it  is  structurally  possible.  Moreover,  several  buildings  have  shown 
that  not  infrequently  elaborate  precautions  have  resulted  disas- 
trously, sometimes  fundamentally,  sometimes  through  the  oversight 
of  details  which  to  casual  consideration  seem  of  minor  importance. 
Here,  as  in  the  acoustics  of  auditoriums,  the  conditions  are  so  com- 
plicated that  only  a  systematic  and  accurately  quantitative  investi- 
gation will  yield  safe  conclusions.  Some  headway,  perhaps  half  a 
year's  work,  little  more  than  a  beginning,  was  made  in  this  investi- 
gation some  years  ago.  Methods  of  measurements  were  developed 
and  some  results  were  obtained.  Within  the  past  month  the  use  of 
a  room  in  a  new  building,  together  with  that  of  the  room  immedi- 
ately below  it,  has  been  secured  for  the  period  of  two  years.  Be- 
tween these  rooms  the  floor  will  be  laid  in  reenforced  concrete  of  two 
thicknesses,  five  inches  and  ten  inches,  in  hollow  tile,  in  brick  arch, 
in  mill  construction,  and  with  hung  ceiling,  and  the  transmission  of 
sound  tested  in  each  case.  The  upper  surface  of  the  floor  will  be 
laid  in  tile,  in  hardwood,  with  and  without  sound-deadening  lining, 
and  covered  with  linoleum  and  cork,  and  its  noise  to  the  tread 
measured. 


MUSICAL  PITCH  217 

However,  such  experiments  hut  lay  the  foundation.  What  is 
needed  are  tests  of  I  lie  walls  and  floors  of  rooms  of  various  sizes,  and 
of  the  more  varied  construction  which  occurs  in  practice,  in  rooms 
connecting  with  offsets  and  different  floor  levels,  —  the  complicated 
condition  of  actual  building  as  against  the  sinii)lified  conditions  of 
an  orderly  experiment.  The  one  will  give  numerical  coeflicicnts, 
the  other,  if  in  sufficiently  full  measure,  will  give  experience  leading 
to  generalization  which  may  be  so  formulated  as  to  be  of  wide  value. 
What  is  therefore  sought  is  the  opportunity  to  exjieriment  in  rooms 
of  varied  but  accurately  known  construction,  especially  where  the 
insulaticm  has  been  successful.  I'nfortunately,  with  modern  build- 
ing materials  acoustical  difficulties  of  all  sorts  are  very  numerous. 


ARCHITECTUKAL  ACOUSTICS' 

Jjecause  familiarity-  with  Ihe  phenomena  of  sound  has  so  far  out- 
stripped the  adequate  study  of  the  jiroblenis  involved,  many  of  them 
have  been  popularly  shrouded  in  a  wholly  unnecessary  mysterj'. 
Of  none,  i)erhaps,  is  this  more  true  than  of  architectural  acoustics. 
The  conditions  surrounding;  the  transmission  of  speech  in  an  en- 
closed auditorium  are  complicated,  it  is  true,  but  are  only  such  as 
will  yield  an  exact  solution  in  the  lifjht  of  adequate  data.  Tt  is,  in 
other  words,  a  rational  engineering  problem. 

The  problem  of  architectural  acoustics  is  necessarily  complex, 
and  each  room  presents  main'  coiidil  ions  which  contribute  to  the 
result  in  a  greater  or  less  degree.  ac(t)rding  to  circumstances.  To 
take  justly  into  account  these  varied  conditions,  the  solution  of  the 
problem  should  be  quantitative,  not  merely  qualitative;  and  to 
reach  its  highest  usefulness  and  the  dignity  of  an  engineering  science 
it  should  be  such  that  its  application  can  precede,  not  merely  follow, 
the  construction  of  the  building. 

In  order  that  hearing  may  be  good  in  any  awditoriiun  it  is  neces- 
sary that  the  .sound  should  be  sufficiently  loud,  that  the  simulta- 
neous components  of  a  complex  sound  should  maintain  their  jiroper 
relative  intensities,  and  that  the  successive  sounds  in  rapidly  moving 
articulation,  eitlu-r  of  si)et'cli  or  of  nuisic,  should  be  dear  and  distinct, 
free  from  each  other  and  from  extraneous  noises.  These  three  are 
the  necessarj',  as  they  are  the  entirely  sufficient,  conditions  for  good 
hearing.  Scientifically  the  proi)lem  involves  three  factors:  rever- 
beration, interference,  and  resonance.  As  an  engineering  j)roblem 
it  involves  the  shape  of  the  auditorium,  its  dimensions,  and  the 
materials  of  which  it  is  composed. 

Sound,  i>eiug  ciiergA',  once  ])roduced  in  a  confined  space,  will 
continue  until  it  is  either  traii-<niitted  by  the  boun<lar>'  walls  or  is 
transformed  into  some  other  kind  of  i-nerg^',  generally  heal.  This 
process  of  decay  is  called  al)sorption.    Thus,  in  the  lecture-rtK>m  of 

'  The  Jouriiul  uf  the  Franklin  Inxlitutc,  Januar}-,  1013. 


220  ARCIIITECTITRAL  ACOUSTICS 

Harvard  rnivorsity,  in  which,  and  in  behalf  of  which,  tliis  investi- 
gation was  begun,  the  rate  of  absorption  was  so  small  that  a  word 
spoken  in  an  ordinary  tone  of  voice  was  audible  for  five  and  a  half 
seconds  afterwards.  During  this  time  even  a  very  deliberate  speaker 
would  have  uttered  the  twelve  or  fifteen  succeeding  syllables.  Thus 
the  successive  enunciations  blended  into  a  loud  sound,  through 
which  and  above  which  it  was  necessary  to  hear  and  distinguish  the 
orderly  progression  of  the  speech.  Across  the  room  this  could  not 
be  done;  even  near  the  speaker  it  could  be  done  only  with  an  effort 
wearisome  in  the  extreme  if  long  maintained.  With  an  audience 
filling  the  room  the  conditions  were  not  so  bad,  but  still  not  tolerable. 
This  may  be  regarded,  if  one  so  chooses,  as  a  process  of  nniltiple  re- 
flection from  walls,  from  ceiling,  and  from  floor,  first  from  one  and 
then  another,  losing  a  little  at  each  reflection  until  ultimately  in- 
audible. This  phenomenon  will  be  called  reverberation,  including, 
as  a  special  case,  the  echo.  It  nuist  be  observed,  however,  that,  in 
general,  reverberation  results  in  a  mass  of  soimd  filling  the  whole 
room  and  incapable  of  analysis  into  its  distinct  reflections.  It  is 
thus  more  difficult  to  recognize  and  impossible  to  locate.  The  term 
"echo"  will  be  reserved  for  that  particular  case  in  which  a  short, 
sharp  sound  is  distinctly  repeated  by  reflection,  either  once  from  a 
single  surface,  or  several  times  from  two  or  more  surfaces.  In  the 
general  case  of  reverberation  we  are  concerned  only  with  the  rate  of 
decay  of  the  sound.  In  the  special  case  of  the  echo  we  are  concerned 
not  merely  wnth  its  intensity,  but  with  the  interval  of  time  elapsing 
between  the  initial  sound  and  the  moment  it  reaches  the  observer. 
In  the  room  mentioned  as  the  occasion  of  this  investigation  no  dis- 
crete echo  was  distinctly  perceptible,  and  the  case  will  serve  ex- 
cellently as  an  illustration  of  the  more  general  type  of  reverberation. 
After  preliminary  gropings,  first  in  the  literature  and  then  with 
several  optical  devices  for  measuring  the  intensity  of  sound,  all 
established  methods  were  abandoned.  Instead,  the  rate  of  decay 
was  measured  by  measuring  what  was  inversely  proportional  to  it, 
—  the  duration  of  audibility  of  the  reverberation,  or,  as  it  will  be 
called  here,  the  duration  of  audibility  of  the  residual  sound.  These 
experiments  may  be  explained  to  advantage  here,  for  they  will  give 
more  clearly  than  would  abstract  discussion  an  idea  of  the  nature 


ARCniTFXTniAL  ACOUSTICS 


221 


of  reverberation.  Broadly  considered,  there  are  two,  and  only  two, 
variables  in  a  room,  —  shape  (including  size)  and  materials  (includ- 
ing furnishings).  In  designing  an  auditorium  an  architect  can  give 
consideration  to  both;  in  r»'j)air  work  for  liad  acoustic  conditions  it 
is  generally  impracticable  to  change  the  shape,  and  only  variations 
in  materials  and  furnishings  are  allowable.  This  wiis,  therefore, 
the  line  of  work  in  this  cas<'.  It  was  evident  that,  other  things  being 
equal,  the  rate  at  which  the  reverlxTation  would  disappear  was 
proi)ortional  to  the  rate  at  which  the  sound  wa.s  absorbed.  The 
first  work,  therefore,  was  to  detennine  the  relative  absorbing  power 


\ 

V 

*h 

«>«. 

►-> 

t^ 

*~- 

-»-. 

^ 

10 

9 

8 
7 
6 

S 
4 
3 
2 
1 

"25  40  60  80  100  120  140  160  140  ZOO  220  240  Z&O  280  300 

Length  of  cushions  in  meters 

Fio.  1.    Curve  showing  the  relation  of  the  duration  of  the  residual 
sound  to  thi-  addiil  absorbing  material. 

of  various  substances,  ^^■ilh  an  organ  pipe  as  a  constant  source  of 
soimd,  and  a  suitable  chronograi)h  for  recording,  the  duration  of 
audibility  of  a  sound  after  the  source  had  ceased  in  tiiis  room  when 
empty  was  found  to  be  o.G'-i  seconds.  All  the  cushions  from  tiie 
seats  in  Sanders  Theatre  were  then  brought  over  and  stored  in  the 
lobby.  On  bringing  into  the  Icctun-room  a  number  of  cushions, 
having  a  total  length  of  8.-2  meters,  the  duration  of  audibility  fell  to 
5.:53  seconds.  Ou  bringing  in  17  meters  the  sound  in  the  room  after 
the  organ  pipe  ceiused  wius  audible  for  l)ut  4.94  stH-onds.  Kvidently 
the  cushions  were  strong  absorbents  and  ra|)idly  improving  the 
room,  at  lea^st  to  the  extent  of  diminishing  the  reverberation.  The 
result  wa.s  interesting  and  the  process  was  contimied.  Little  by 
little  the  cushions  were  brought  into  the  riMjm,  and  each  lime  the 


222 


ARCHITPXTURAL  ACOUSTICS 


duration  of  audibility  was  measured.  When  all  the  seats  (436  in 
number)  were  covered,  the  sound  was  audible  for  2.03  seconds. 
Then  the  aisles  were  covered,  and  then  the  platform.  Still  there 
were  more  cusliioiis,  -  almost  half  as  many  more.  These  were 
broufjhl  into  the  room,  a  few  at  a  time,  as  before,  and  draped  on  a 
scafTolding  that  had  been  erected  around  the  room,  the  duration  of 
the  sound  being  recorded  each  time.  Finally,  when  all  the  cushions 
from  a  theatre  seating  nearly  fifteen  hundred  persons  were  placed 
in  tlie  room  —  covering  the  seats,  the  aisles,  the  platform,  the  rear 
wall  to  the  ceiling  —  tiie  duration  of  audibility  of  the  residual  sound 


•g 


■ 

\ 

\ 

\ 

s 

\ 

s 

V, 

' — , 

— 

— 

— 

— 

0  80 

Walls 


160 


240 


320  400 

Cushions 


480 


560 


Fig.  2.  Curve  5  plotted  as  part  of  its  corresponding  rectangular 
hj-perbola.  The  solid  part  was  determined  experimentally; 
the  displacement  of  this  to  the  right  measures  the  absorbing 
power  of  the  walls  of  the  room. 

was  1.14  seconds.  This  experiment,  requiring,  of  course,  several 
nights'  work,  having  been  completed,  all  the  cushions  were  removed 
and  the  room  was  in  readiness  for  the  test  of  other  absorbents.  It 
was  evident  that  a  standard  of  comparison  had  been  established. 
Curtains  of  chenille,  1.1  meters  wide  and  17  meters  in  total  length, 
were  draped  in  the  room.  The  duration  of  audibility  was  then  4.51 
seconds.  Turning  to  the  data  that  had  just  been  collected,  it  ap- 
peared that  this  amount  of  chenille  was  equivalent  to  30  meters  of 
Sanders  Theatre  cushions.  Oriental  rugs  (Herez,  Demirjik,  and 
Ilindoostanee)  were  tested  in  a  similar  manner,  as  were  also  cretonne 
cloth,  canvas,  and  hair  felt.     Similar  experiments,  but  m  a  smaller 


ARCHITECTURAL  ACOUSTICS  223 

room,  determined  the  absorbing  power  of  a  man  and  of  a  woman, 
always  by  determining  the  number  of  running  meters  of  Sanders 
Theatre  cushions  that  would  produce  the  same  effect.  This  process 
of  comparing  two  absorbents  ])y  actually  substituting  one  for  the 
other  is  laborious,  and  it  is  given  lu-re  only  to  show  the  first  steps 
in  the  development  of  a  method.  Without  going  into  details,  it  is 
sufficient  here  to  say  that  this  method  was  so  perfected  as  to  give 
not  merely  relative,  but  absolute,  coefficients  of  absorption. 

In  this  manner  a  number  of  coefficients  of  absorption  were  de- 
termined for  objects  and  materials  which  could  be  brought  into 
and  removed  from  the  room,  for  sounds  having  a  pitch  an  octave 
above  middle  C.  In  the  following  table  the  numerical  values  are 
the  absolute  coefficients  of  the  absorption: 

Oil  paintings,  inclusive  of  frames 28 

Carpel  rugs 20 

Oriental  rugs,  extra  heavy 29 

Cheesecloth   019 

Cretonne  <lotli 15 

Shelia  curtains 23 

Hair  felt,  2.5  cm.  thick,  8  cm.  from  wall 78 

Cork,  i.3  cm.  thick,  loose  on  floor 16 

Linoleum,  loose  on  floor 12 

When  the  objects  are  not  extended  surfaces,  such  as  carpets  or 

rugs,  but  essentially  spacial  units,  it  is  not  easy  to  express   the 

absorption  as  an  absolute  coefficient.     In  the  following  table  the 

al)sori)tion  of  each  object  is  expressed  in  terms  of  a  square  meter  of 

complete  absorption: 

Audience,  per  person 44 

Isolated  woman 54 

Isohite<l  man 48 

Plain  ash  settees 039 

I'lain  ash  settees,  per  single  scat 0077 

riain  ash  chairs,  "  hcnt  w(mm1  " 0082 

I  pliolstercd  sctlecs,  hair  and  leather 1.10 

1  pholstcreil  si'tlecs,  per  single  seat iJS 

I'pholstcriil  chairs  similar  in  style SO 

Hair  cushions,  per  .seat 21 

Klastic  fell  cushions,  [)er  scut 20 

Of  tvcu  gnahr  importance  was  tlie  (ittermination  of  tlic  ct)- 
cfficient  of  ab.sori)fion  of  fl(M)rs,  ceilings,  and  wall-surfa<vs.      TIk- 


224 


ARCHITECTURAL  ACOUSTICS 


accoinplishiiK'iil  of  this  called  for  a  very  considerable  extension  of 
the  method  adopted.  If  the  reverberation  in  a  room  as  changed 
by  the  addition  of  absorbing  material  be  plotted,  the  resulting 
curve  will  be  found  to  be  a  portion  of  an  hyperbola  with  displaced 
axes.  An  example  of  such  a  curve,  as  obtained  in  the  lecture- 
room  of  the  Fogg  Art  Museum,  in  Cambridge,  is  plotted  in  the 
diagram.  Fig.  1.  If  now  the  origin  of  this  curve  be  displaced  so 
that  the  axes  of  coordinates  are  the  asymptotes  of  the  rectangular 
hjT)erbola,  the  displacement  of  the  origin  measures  the  initial  ab- 


10 

\ 

5;;  ;    \ 

1 

\ 

\ 

> 

\ 

\ 

"2    ft 

.^ 

s. 

^N, 

1'.;  i*    \ 

\ 

\ 

\ 

s 

'--, 

_a 

"?lr 

\ 

'\ 

\ 

*x^ 

V 

\. 

"--- 

.„. 

a     4 

.2 

\^\ 

\ 

\ 

\ 

"■s 

\ 

■--^ 

"~" 

---^ 

-12 

£     3 

a     2 

'> 

^,^ 

Jv'S. 

^v 

^-.. 

■"8. 

^9- 

~10, 

-IV 





\^^ 

-^-' 

'r-'-s 

-- 



""■ 



-  — 

— 

;  — 

l"-- 

IT.: 

-'V,- 

-%=-=i 

^--^=i 

-"j:";^ 

r.^V 

r.-»r 

fSi- 

rC-i>^ 

:-i-z4: 

-z=iz' 

0         10  20  30  40  SO  60  70  80  90  100  110  120  130  140  IGO 
120     leO     240     300     360     420 
540     720     900     1080    1360 

Total  absorbing  material 

Fig.  3.  The  curves  of  Figs.  8  and  9  entered  as  parts  of  their  corre- 
sponding rectangular  hj-perbolas.  Three  scales  are  employed  for 
the  volumes,,  by  groups  1-7,  8-11,  and  12. 

sorbing  power  of  the  room,  its  floors,  walls,  and  ceilings.  Such 
experiments  were  carried  out  in  a  large  number  of  rooms  in  which 
the  diflFerent  component  materials  entered  in  very  different  degrees, 
and  an  elimination  between  these  different  experiments  gave  the 
following  coefficient  of  absorption  for  different  materials: 

Open  window 1.000 

Wood  sheathing  (hard  pine) 061 

Plaster  on  wood  lath 034 

Plaster  on  wire  lath 033 

Glass,  single  thickness 027 

Plaster  on  tile 025 

Brick  set  in  Portland  cement 025 


ARCIIITECTI'RAL  ACOUSTICS 


225 


If  the  experiments  in  these  rooms  are  plotted  in  a  single  dia- 
gram, the  result  is  a  family  of  hyperbolae  showing  a  very  interesting 
relationship  to  the  volumes  of  the  rooms.  Indeed,  if  from  these 
hj'perholas  the  parameter,  which  etjuals  the  product  of  the  co- 
ordinates, be  deternn'ned,  it  will  be  found  to  be  linearly  j)ropor- 
tional  to  the  volume  of  the  room.  These  results  are  plotted  in 
Fig.  4,  showing  how  strict  the  proportionality  is  even  over  a  very 
great  range  in  vohinic.     We  have  thus  at  hand  a  ready  method  of 


u 


ISO  - 


•S  100 


.<L 

/ 

°u 

/ 

MM 

lOMo 

12»00 

1 

V 

A 

A 

/ 

1200 

1800 

2400 

30C0 

3600 

4300 

/ 

4 
1 

A 

a 

I      : 

1 

I 

600  800  lOOO 

Volumes  of  rooms 


IMO 


Fig.  4.     The   parameter,  k,  plolled  against  the  volumes    of  the 
rooms,  showing  the  two  proportional. 


calculating  the  reverberation  for  any  room,  its  volume  and  the 
materials  of  which  it  is  composed  being  known. 

The  first  five  years  of  tlie  investigation  were  devoted  to  violin 
C,  the  C  an  octave  above  middle  C,  having  a  vibration  frequency 
of  512  vibrations  i)er  .second.  This  i)iteli  was  cho.sen  becau.se,  in 
the  art  of  telephony,  it  was  regarded  at  liiat  lime  as  the  character- 
istic pitch  determining  the  conditions  of  articulate  speech.  The 
planning  of  Syni|)h(my  Hall  in  Hoston  forced  an  extension  of  this 
investigation  to  notes  over  tlie  whole  range  of  tlie  musical  .scale, 
three  octaves  below  and  three  octaves  above  violin  ('. 

In  the  verv-  nature  of  the  problem,  the  most  important  dalinn 
is  the  alisorplion  coeHicienl  of  an  audience,  and  the  determination 
of  thi>  was  tlie  first   task  undtTtak.ii.     \\\    nuaii-  of  a   Ifctun-  on 


i^2G  ARCHITECTOiAL  ACOUSTICS 

one  of  llie  recent  de\elopments  of  physics,  wireless  telegraphy,  an 
audience  was  thus  drawn  together  and  at  the  end  of  the  lecture 
requested  to  remain  for  the  experiment.  In  this  attempt  the  effort 
was  made  to  determine  Die  coefficients  for  the  five  octaves  from 
C2I28  to  CV2048,  including  notes  E  and  G  in  each  octave.  For 
several  reasons  the  experiment  was  not  a  success.  A  threatening 
thunderstorm  made  the  audience  a  small  one,  and  the  sultriness  of 
the  atmosphere  made  open  windows  necessary,  while  the  attempt 
to  cover  so  many  notes,  thirteen  in  all,  prolonged  the  experiment 
beyond  the  endurance  of  the  audience.  While  tliis  experiment 
failed,  another  the  following  summer  was  more  successful.  In  the 
year  that  had  elapsed  the  necessity  of  carrj-ing  the  investigation 
further  than  the  limits  intended  became  evident,  and  now  the  ex- 
periment was  carried  from  Ci64  to  C7409G,  but  included  only  the 
C  notes,  seven  notes  in  all.  Moreover,  bearing  in  mind  the  experi- 
ences of  the  previous  summer,  it  was  recognized  that  even  seven 
notes  would  come  dangerously  near  overtaxing  the  patience  of  the 
audience.  Inasmuch  as  the  coefficient  of  absorption  for  C4512  had 
already  been  determined  six  years  before,  in  the  investigations 
mentioned,  the  coefficient  for  this  note  was  not  redetermined.  The 
experiment  was  therefore  carried  out  for  the  lower  three  and  the 
upper  three  notes  of  the  seven.  The  audience,  on  the  night  of  this 
experiment,  was  much  larger  than  that  which  came  the  previous 
summer,  the  night  was  a  more  comfortable  one,  and  it  was  possible 
to  close  the  windows  during  the  experiment.  The  conditions  were 
thus  fairly  satisfactory.  In  order  to  get  as  much  data  as  possible,  and 
in  as  short  a  time,  there  were  nine  observers  stationed  at  different 
points  in  the  room.  These  observers,  whose  kindness  and  skill  it  is 
a  pleasure  to  acknowledge,  had  prepared  themselves,  by  previous 
practice,  for  this  one  experiment.  The  results  of  the  experiment 
are  shown  on  the  lower  cur^'e  in  Fig.  5.  This  curve  gives  the  co- 
efficient of  absorption  per  person.  It  is  to  be  observed  that  one  of 
the  points  falls  clearly  off  the  smooth  curve  drawn  tlirough  the  other 
points.'  The  observations  on  which  this  point  is  based  were,  how- 
ever, much  disturbed  by  a  street  car  passing  not  far  from  the  build- 
ing, and  the  departure  of  this  observation  from  the  curve  does  not 

'  This  point,  evidently  on  the  ordinate  Cs,  is  omitted  in  the  original  cut.  —  Editor. 


ARCHITECTIRAL  ACOUSTICS 


227 


inilicate  a  real  departure  in  the  coefficient,  nor  should  it  cast  much 
doubt  on  the  rest  of  the  work,  in  view  of  the  circumstances  under 
which  it  was  secured.    Counteracting  the,  perhaps,  bad  impression 


.0 

-^ 

.9 

/ 

r 

.U 

/ 

/ 

.7 

/ 

.6 

/ 

.5 

/ 

^ 

.4 

/ 

/' 

.3 

/ 

.2 

/ 

.1 

c, 


c. 


c, 


c. 


c. 


c, 


Flii-  J-  1  '»-■  uljsorbiiit;  powrr  of  an  uuiiieiicv  fur  iliircriiil 
notes.  Till'  lower  curve  repre«Mits  tlie  iibsorliinK  power 
of  uii  audience  per  person.  Tlie  upper  curve  represents 
llie  absorbing  power  of  an  audience  per  sipinre  meter 
OS  ordinarily  sealed.  The  vertical  ordinates  arc  ex- 
pre.s-sed  in  terms  of  total  absorption  by  a  square  meter 
of  surface.  I'or  the  upper  curve  tlie  ordinales  ore  thus 
the  onliiuiry  cwllicieiits  of  absorption.  The  several 
notes  ore  at  octave  intervals  as  follows:  ('ilU.  CM<8, 
C,  (middle  C)  i5«.  ('.51i,  (\\VH.\.  C.itm.  Cj+OUO. 

wliich  thi.s  point  may  K've,  it  i.s  a  coii.sidtralile  .sali.sfaetion  to  note 
how  accurately  the  |)oinl  for  C45H,  determined  .sL\  years  U-fore  by 
a  dilTereiit  set  of  observers,  falls  on  the  smooth  curve  through  the 


-228  ARCHITECTURAL  ACOUSTICS 

remaining  points.  In  the  audience  on  which  these  observations 
wore  taken  there  were  77  women  and  105  men.  The  courtesy  of 
the  audience  in  remaining  for  the  experiment  and  the  really  re- 
markable silence  which  they  maintained  are  gratefully  acknowl- 
edged. 

The  next  experiment  was  on  the  determination  of  the  absorp- 
tion of  sound  by  wood  sheathing.  It  is  not  an  easy  matter  to  find 
conditions  suitable  for  this  experiment.  The  room  in  which  the 
absorption  by  wood  sheathing  was  determined  in  the  earlier  ex- 
|)eriments  was  not  available  for  these.  It  was  available  then  only 
because  the  building  was  new  and  empty.  When  these  more  elabo- 
rate experiments  were  under  way  the  room  became  occupied,  and 
in  a  manner  that  did  not  admit  of  its  being  cleared.  Quite  a  little 
searching  in  the  neighborhood  of  Boston  failed  to  discover  an  en- 
tirely suitable  room.  The  best  one  available  adjoined  a  night 
lunch  room.  The  night  lunch  was  bought  out  for  a  couple  of 
nights,  and  the  experiment  was  tried.  The  work  of  both  nights 
was  much  disturbed.  The  traffic  past  the  building  did  not  stop 
until  nearly  two  o'clock,  and  began  again  at  four.  The  interest  of 
those  passing  on  foot  throughout  the  night,  and  the  necessity  of 
repeated  explanations  to  the  police,  greatly  interfered  with  the 
work.  This  detailed  statement  of  the  conditions  under  which  the 
experiment  was  tried  is  made  by  way  of  explanation  of  the  irregu- 
larity of  the  observations  recorded  on  the  curve,  and  of  the  failure 
to  carry  this  particular  line  of  work  further.  The  first  night  seven 
points  were  obtained  for  the  seven  notes  Ci64  to  C74096.  The  re- 
duction of  these  results  on  the  following  day  showed  variations 
indicative  of  maxima  and  minima,  which,  to  be  accurately  located, 
would  require  the  determination  of  intermediate  points.  In  the 
experiment  the  following  night  points  were  determined  for  the  E 
and  G  notes  in  each  octave  between  Col28  and  C62048.  Other 
points  would  have  been  determined,  but  time  did  not  permit.  It 
is  obvious  that  the  intermediate  points  in  the  lower  and  in  the 
higher  octave  were  desirable,  but  no  pipes  were  to  be  had  on  such 
short  notice  for  this  part  of  the  range,  and  in  their  absence  the  data 
could  not  be  obtained.  In  the  diagram.  Fig.  6,  the  points  lying  on 
the  vertical  lines  were  determined  the  first  night.    The  points  lying 


ARCHITECTURAL  ACOUSTICS 


229 


between  the  vertical  lines  were  determined  the  second  night.    The 
accuracy  with  which  these  points  fall  on  a  smooth  curve  is,  perhaps, 

.12 


.U 

.10 
.09 
.08 
.07 
.06 
.05 
.04 
.03 
.02 
.01 


> 


c. 


c. 


c. 


c. 


c, 


Fig.  (i.  The  absorbing  powrr  of  wood  sheathing,  two  centi- 
meters thick,  North  Carolina  pine.  The  ob.servations 
were  made  under  very  unsuitable  eiinilitions.  The 
abiiorplioii  is  here  due  almost  wholly  to  yieliiing  of  the 
sheathing  as  a  wholi',  the  surface  bi'ing  shellacked, 
smooth,  and  non-porous.  The  curve  shows  one  point 
of  resonance  within  the  range  tested,  anil  the  prob- 
ability of  anoth<T  point  of  resonance  alK>V4>.  It  is  not 
possible  now  lo  learn  as  much  in  regard  to  the  framing 
anil  arrangement  of  the  studding  in  thi'  particular  room 
tested  us  is  desirable.     (>  (middle  (')  iM. 


O30  ARCHITECTURAL  ACOUSTICS 

all  that  could  be  expected  in  view  of  the  difficulty  under  which  the 
observations  were  conducted  and  the  linuted  time  available.  One 
point  in  particular  falls  far  off  from  this  curve,  the  point  for  C3256, 
by  an  amount  which  is,  to  say  the  least,  serious,  and  which  can  be 
justified  only  by  tlie  conditions  xmder  which  the  work  was  done. 
The  general  trend  of  the  curve  seems,  however,  established  beyond 
reasonable  doubt.  It  is  interesting  to  note  that  there  is  one  point 
of  maximum  absorption,  which  is  due  to  resonance  between  the 
walls  and  the  sound,  and  that  this  point  of  maximum  absorption 
lies  in  the  lower  part,  though  not  in  the  lowest  part,  of  the  range  of 
pitch  tested.  It  would  have  been  interesting  to  determine,  had  the 
time  and  facilities  permitted,  the  shape  of  the  curve  beyond  C74096, 
and  to  see  if  it  rises  indefinitely,  or  shows,  as  is  far  more  likely,  a 
succession  of  maxima. 

The  experiment  was  then  directed  to  the  determination  of  the 
absorption  of  sound  by  cushions,  and  for  this  purpose  return  was 
made  to  the  constant-temperature  room.  Working  in  the  manner 
indicated  in  the  earlier  papers  for  substances  which  could  be  carried 
in  and  out  of  a  room,  the  curves  represented  in  Fig.  7  were  obtained. 
Curve  1  shows  the  absorption  coefficient  for  the  Sanders  Theatre 
cushions,  with  which  the  whole  investigation  was  begun  ten  years 
ago.  These  cushions  were  of  a  particularly^  open  grade  of  packing, 
a  sort  of  wiry  grass  or  vegetable  fiber.  They  were  covered  with 
canvas  ticking,  and  that,  in  turn,  with  a  very  thin  cloth  covering. 
Curve  2  is  for  cushions  borrowed  from  the  Phillips  Brooks  House. 
They  were  of  a  high  grade,  filled  with  long,  curly  hair,  and  covered 
with  canvas  ticking,  which  was,  in  turn,  covered  by  a  long  nap 
plush.  Curve  3  is  for  the  cushions  of  Appleton  Chapel,  hair  covered 
with  a  leatherette,  and  showing  a  sharper  maximum  and  a  more 
rapid  diminution  in  absorption  for  the  higher  frequencies,  as  would 
be  expected  under  such  conditions.  Curve  4  is  probably  the  most 
interesting,  because  for  more  standard  commercial  conditions  ordi- 
narily used  in  churches.  It  is  to  be  observed  that  all  four  curves 
fall  off  for  the  higher  frequencies,  all  show  a  maximum  located 
within  an  octave,  and  three  of  the  curves  show  a  curious  hump  in 
the  second  octave.  This  break  in  the  curve  is  a  genuine  phenomenon, 
as  it  was  tested  time  after  time.    It  is  perhaps  due  to  a  secondary 


ARCHITECTLTRAL  ACOUSTICS 


231 


resonance,  and  it  is  to  be  observed  that  it  is  the  more  pronounced  in 
those  curves  that  have  the  sharper  resonance  in  their  principal 
maxima. 

1.0 


.9 


.6 


.3 


A 

\ 

//' 

f 

\ 

^ 

•f 

^ 

\ 

\ 

/ 

// 

\ 

\ 

\\ 

/  ^ 

■* 

V 

\ 

\ 

^ 

7 

\ 

^ 

/ 

\ 

\ 

c, 


c. 


c. 


c. 


c. 


c, 


FiQ.  7.  The  absorbing  power  of  cushions.  Curve  1  is 
for  "Sanders  Theatre"  cushions  of  wiry  vegetable 
6ber,  covered  with  canvas  ticking  and  a  thin  cloth. 
Curve  i  is  for  "Brooks  House"  cushions  of  long  hair, 
covered  with  the  same  kind  of  ticking  and  plush. 
Curve  3  is  for  ".\ppleton  Chapel"  cushions  of  hair, 
covered  with  ticking  and  a  thin  liallnTctle.  Curve  4 
is  for  the  elastic  felt  cushions  of  rinniiiiTce.  of  clastic 
cotton,  covered  with  ticking  and  short  nap  plush.  The 
absorbing  power  is  per  sipiare  meter  of  surface. 
Ci  (middle  C)  tbO. 

In  both  articuhile  speccli  and  in  music  the  source  of  soimd  is 
raj)i(IIy  and.  in  fjcncral.  abriii)lly  cliaiiijint;  in  pitch,  quality,  and 
loudne.**-'^.     In   niii.sic  one  i)itch  is  held  duriny  the  leiiglh  of  a  note. 


232  ARCHITECTUKAL  ACOUSTICS 

In  articulate  speech  the  unit  or  element  of  constancy  is  the  syllable. 
Indeed,  in  speech  it  is  even  less  than  the  length  of  a  syllable,  for 
the  open  vowel  sound  which  forms  the  body  of  a  syllable  usually 
has  a  consonantal  opening  and  closing.  During  the  constancy  of 
an  element,  either  of  music  or  of  speech,  a  train  of  sound-waves 
spreads  spherically  froTU  the  source,  just  as  a  train  of  circular 
waves  spreads  outward  from  a  rocking  boat  on  the  surface  of  still 
water.  Different  portions  of  this  train  of  spherical  waves  strike 
different  surfaces  of  the  auditorium  and  are  reflected.  After  such 
reflection  they  begin  to  cross  each  other's  paths.  If  their  paths 
are  so  differejit  in  length  that  one  train  of  waves  has  entirely  passed 
before  the  other  arrives  at  a  particular  point,  the  only  phenomenon 
at  that  point  is  prolongation  of  the  sound.  If  the  space  between 
the  two  trains  of  waves  be  sufficiently  great,  the  effect  will  be  that 
of  an  echo.  If  there  be  a  number  of  such  trains  of  waves  thus  widely 
spaced,  the  effect  will  be  that  of  multiple  echoes.  On  the  other 
hand,  if  two  trains  of  waves  have  traveled  so  nearly  equal  paths 
that  they  overlap,  thej^  will,  dependent  on  the  difference  in  length 
of  the  paths  which  they  had  traveled,  either  reenforce  or  mutually 
destroy  each  other.  Just  as  two  equal  trains  of  water-waves  cross- 
ing each  other  may  entirely  neutralize  each  other  if  the  crest  of  one 
and  the  trough  of  the  other  arrive  together,  so  two  sounds,  coming 
from  the  same  source,  in  crossing  each  other  may  produce  silence. 
This  phenomenon  is  called  interference,  and  is  a  common  phenom- 
enon in  all  types  of  wave-motion.  Of  course,  this  phenomenon  has 
its  complement.  If  the  two  trains  of  water-waves  so  cross  that  the 
crest  of  one  coincides  with  the  crest  of  the  other  and  trough  with 
trough,  the  effects  will  be  added  together.  If  the  two  sound-waves 
be  similarly  retarded,  the  one  on  the  other,  their  effects  will  also 
be  added.  If  the  two  trains  of  waves  be  equal  in  intensity,  the 
combined  intensity  will  be  quadruple  that  of  either  of  the  trains 
separately,  as  above  explained,  or  zero,  depending  on  their  relative 
retardation.  The  effect  of  this  phenomenon  is  to  produce  regions 
in  an  auditorium  of  loudness  and  regions  of  comparative  or  even 
complete  silence.  It  is  a  partial  explanation  of  the  so-called  deaf 
regions  in  an  auditorium. 


ARCHITECTURAL  ACOUSTICS 


233 


It  is  not  difficult  to  observe  this  phenomenon  directly.  It  is 
difficult,  however,  to  measure  and  record  the  phenomenon  in  such 
a  manner  as  to  permit  of  an  accurate  chart  of  the  result.  Without 
going  into  the  details  of  the  method  employed,  the  result  of  these 


^--^^^^ ^Z^V_^ 


FlO.  H.  DLslrihuliim  of  iiili-ii.sily  on  the  head  level  ill  a  room 
with  a  barrel-shiipoil  ceiling,  with  center  of  curvature  on  the 
floor  level. 


measurements  for  a  room  very  similar  lo  llu-  (  ougregatioual  (  luircli 
in  Naugatuck,  Connecticut,  is  shown  in  the  accompanying  eliart. 
The  room  exixTiniented  in  was  a  siinj)le,  rectangular  room  with 
plain  side  walls  and  ends  and  with  a  barrel  or  cylindrical  ceiling. 
The  result  is  clearly  repre.senled  in  Fig.  8,  in  which  the  intensity 


234 


ARCHITECTniAL  ACOUSTICS 


of  tlu-  sound  has  l)eon  indicated  by  contour  linos  in  the  manner 
eini)loyed  in  the  drawing  of  tlie  geodetic  survey  maps.  The  phenom- 
enon indicated  in  these  diagrams  was  not  ephemeral,  hut  was  con- 
stant so  long  as  the  source  of  sound  continued,  and  repeated  itself 
with  almost  perfect  accuracy  day  after  day.    Nor  was  the  phenom- 


Fio.  9 


Fig. 11 


Fig. 10 


Fig.  1^ 


enon  one  which  could  be  observed  merely  instrumentally.  To  an 
observer  moving  about  in  the  room  it  was  quite  as  striking  a  j)henom- 
enon  as  the  diagrams  suggest.  At  the  points  in  the  room  indicated 
as  high  ma-xima  of  intensity  in  the  diagram  the  sound  was  so  loud 
as  to  be  disagreeable,  at  other  points  so  low  as  to  be  scarcely  audible. 
It  should  be  added  that  this  distribution  of  intensity  is  with  the 
source  of  sound  at  the  center  of  the  room.  Had  the  source  of  sound 
been  at  one  end  and  on  the  axis  of  the  cylindrical  ceiling,  the  dis- 


ARCHITEC  TIRAL  ACOUSTICS 


235 


tribution  of  intensity  would  still  have  been  bilaterally  symmetrical, 
but  not  symmetrical  about  the  transverse  axis. 

When  a  source  of  sound  is  maintained  constant  for  a  sufficiently 
long  time  —  a  few  seconds  will  ordinarily  suffice  the  sound  l)ecomes 
steady  at  everj'  point  in  the  room,    'i'lie  distribution  of  the  intensity 


Kk:.  IM 


Fig. 15 


I'u,.  U 


Vu..  Hi 


of  sovmd  iiiidii-  llicse  conditions  is  called  the  interference  system, 
for  that  ])arlicular  ncttc,  of  the  room  or  space  in  ciuestion.  If  tlic 
source  of  sound  is  suddenly  stojjped,  it  re((uires  some  time  fur  llic 
sound  in  the  room  to  be  ab.sorbeil.  This  prolongation  of  sound  after 
the  source  has  ceased  is  calle<l  reverberation.  If  the  source  of  sound, 
instead  of  being  nuiinlained,  is  short  and  sharp,  it  travels  as  a  ilis- 
crete  wave  or  grou])  of  waves  about  the  room,  reflected  from  wall  to 


236  ARCHITECTURAL  ACOUSTICS 

wall,  jjioducing  echoes.  In  the  Greek  theatre  there  was  ordinarily 
but  one  echo,  "doubling  the  case  ending,"  while  in  the  modern 
auditorium  there  are  many,  generally  arriving  at  a  less  interval  of 
time  after  the  direct  sound  and  therefore  less  distinguishable,  but 
stronger  and  therefore  more  disturbing. 

The  formation  and  the  j)ropagation  of  echoes  may  be  admirably 
studied  by  an  adaptation  of  the  so-called  schlieren-Methode  device 
for  photographing  air  disturbances.  It  is  sufficient  here  to  say  that 
the  adaptation  of  this  method  to  the  problem  in  hand  consists  in 
the  construction  of  a  model  of  the  auditorium  to  be  studied  to 
proper  scale,  and  investigating  the  propagation  through  it  of  a 
proportionally  scaled  sound-wave.  To  examine  the  formation  of 
echoes  in  a  vertical  section,  the  sides  of  a  model  are  taken  off  and, 
as  the  .sound  is  passing  through  it,  it  is  illuminated  instantaneously 
by  the  light  from  a  very  fine  and  somewhat  distant  electric  spark. 
In  the  preceding  illustrations,  reduced  from  the  photographs, 
the  enframing  silhouettes  are  shadows  cast  by  the  model,  and  all 
within  are  direct  photographs  of  the  actual  soimd-wave  and  its 
echoes.  The  four  photographs  show  the  sound  and  its  echoes  at 
different  stages  in  their  propagation  through  the  room,  the  particu- 
lar auditorium  under  investigation  being  the  New  Theatre  in  New 
York.  It  is  not  difficult  to  identify  the  master  wave  and  the  vari- 
ous echoes  which  it  generates,  nor,  knowing  the  velocity  of  sound, 
to  compute  the  interval  at  which  the  echo  is  heard. 

To  show  the  generation  of  echoes  and  their  propagation  in  a 
horizontal  plane,  the  ceiling  and  floor  of  the  model  are  removed  and 
the  photograph  taken  in  a  vertical  direction.  The  photographs 
shown  in  Figs.  13  to  16  show  the  echoes  produced  in  the  horizontal 
plane  passing  through  the  marble  parapet  in  front  of  the  box. 

While  these  several  factors,  reverberation,  interference,  and 
echo,  in  an  auditorium  at  all  complicated  are  themselves  compli- 
cated, nevertheless  they  are  capable  of  an  exact  solution,  or,  at 
least,  of  a  solution  as  accurate  as  are  the  architect's  plans  in  actual 
construction.  And  it  is  entirely  possible  to  calculate  in  advance  of 
construction  whether  or  not  an  auditorium  will  be  good,  and,  if  not, 
to  determine  the  factors  contributing  to  its  poor  acoustics  and  a 
method  for  their  correction. 


10 


THE  INSULATION  OF   SOUND  ^ 

1  HE  insulation  of  sound  as  an  unsolved  prohk-m  in  architectural 
acoustics  was  first  brought  to  the  writer's  attention  by  the  New 
England  Conservatory  of  Music,  immediately  after  its  completion 
in  1904,  and  almost  simultaneously  in  connection  with  a  private 
house  which  had  just  been  c()nii)leted  in  New  York.  A  few  years 
later  it  was  renewed  by  the  Institute  of  ^Musical  Art  in  New  York. 
In  the  construction  of  all  three  buildings  it  had  been  regarded  as 
particularly  important  that  communication  of  sound  from  room  to 
room  should  be  avoided,  and  methods  to  that  end  had  been  em- 
ployed which  were  in  every  way  reasonable.  The  results  showed 
that  in  this  i)hase  of  architectural  acoustics  also  there  had  not  been 
a  sufficiently  searching  and  practical  investigation  and  that  there 
were  no  experimental  data  on  which  an  architect  could  rely.  As 
these  buildings  were  the  oc-c-asion  for  beginning  this  investigation, 
and  were  both  instructive  and  suggestive,  they  are,  with  the  con- 
sent of  the  architects,  discussed  here  at  some  length. 

The  special  method  of  construction  employed  in  the  New  England 
Conservatory*  of  Music  was  suggested  to  the  architects  by  the  Trus- 
tees of  the  Conservators'.  The  floor  of  each  room  was  of  semi-fire- 
proof construction,  cement  between  iron  girtlers,  on  this  a  layer  of 
plank,  on  tliis  j)apcr  lining,  and  on  top  of  this  a  floor  of  hard  pine. 
Between  each  room  for  violin,  piano,  or  vocal  lessons  was  a  com- 
])()und  wall,  constructed  of  two  i)artitions  with  an  unobstructed  air 
space  l)et\veen  tiieui.  Each  partition  was  of  two-inch  plaster  block 
.set  u|)right,  with  the  finishing  plaster  applied  directly  to  the  block. 
The  walls  surrounding  tlic  organ  rooms  were  of  tluce  such  ])artifions 
separated  by  two-inch  air  spaces.  In  eacli  air  space  was  a  con- 
tinuous layer  of  deadening  cloth.  The  scheme  was  carried  out  con- 
sistently and  witli  full  regard  to  details,  yet  lessons  conducted  in 
adjacent  rooms  were  (lislinl)ing  In  cacli  ollu-r. 

'  Till-  UriiklmililiT,  vul.  xxiv,  no.  i,  Fcbruury,  1015. 
137 


238  THE  INSULATION  OF  SOUND 

It  is  always  easier  to  explain  why  a  method  does  not  work  than 
to  know  in  advance  whether  it  will  or  will  not.  It  is  especially  easy 
to  explain  why  it  docs  not  work  when  not  under  the  immediate  neces- 
sity of  correcting  it  or  of  supplying  a  better.  This  lighter  role  of  the 
irresponsible  critic  was  alone  invited  in  the  case  of  the  New  England 
Conservatorj'  of  ^lusic,  nor  will  more  be  ventured  at  the  present 
moment. 

There  is  no  question  whatever  that  the  fundamental  considera- 
tion on  which  the  device  hinged  was  a  soimd  one.  Any  discontinuity 
diminishes  the  transmission  of  sovuid;  and  the  transition  from 
masonrj'  to  air  is  a  discontinuity  of  an  extreme  degree.  Two  solid 
masonrj'  walls  entirely  separated  by  an  air  space  furnish  a  vastly 
better  sound  insulation  than  either  wall  alone.  On  the  other  hand, 
the  problem  takes  on  new  aspects  if  a  masonry  wall  be  replaced  by 
a  series  of  screen  walls,  each  light  and  flexible,  even  though  they 
aggregate  in  massiveness  the  solid  wall  which  they  replace.  More- 
over, such  screen  walls  can  rarely  be  regarded  as  entirely  insulated 
from  each  other.  Granting  that  accidental  commimication  has 
nowhere  been  established,  through,  for  example,  the  extrusion  of 
plaster,  the  walls  are  of  necessity  in  communication  at  the  floor,  at 
the  ceiling,  at  the  sides,  or  at  the  door  jambs;  and  the  connection  at 
the  floor,  at  least,  is  almost  certain  to  be  good.  Further,  and  of  ex- 
treme importance,  given  any  connection  at  all,  the  thinness  of  the 
screen  walls  renders  them  like  drumheads  and  capable  of  large 
response  to  small  excitation. 

It  may  seem  a  remote  parallel,  but  assimie  for  discussion  two 
buildings  a  quarter  of  a  mile  apart.  With  the  windows  closed,  no 
ordinary  sound  in  one  building  could  be  heard  in  the  other.  If, 
however,  the  buildings  were  connected  by  a  single  metal  wire 
fastened  to  the  centers  of  window  panes,  it  would  be  possible  not 
merely  to  hear  from  within  one  building  to  within  the  other,  but 
with  care  to  talk.  On  the  other  hand,  had  the  wires  been  connected 
to  the  hea\'j'  masonry  walls  of  the  two  buildings,  such  communica- 
tion wovdd  have  been  impossible.  This  hj-pothetical  case,  though 
extreme,  indeed  perhaps  the  better  because  of  its  exaggeration,  will 
serve  to  analyze  the  problem.  Here,  as  in  everj'  case,  the  transmis- 
sion of  sound  involves  three  steps,  —  the  taking  up  of  the  vibration. 


THE  INSITATION  OF  SOT'XD  239 

the  function  of  the  nearer  window  pane,  its  transmission  by  the  wire, 
and  its  coniniunication  to  the  air  of  the  receiving  room  by  the  remote 
window.  The  three  functions  may  be  combined  into  one  wlien  a 
solid  wall  separates  the  two  rooms,  the  taking  up,  transmitting;,  and 
emitting  of  tlie  sound  being  scarcely  separable  processes.  On  the 
other  hand,  they  are  often  clearly  separable,  as  in  the  case  of  nndtiple 
screen  walls. 

In  the  case  of  a  solid  masonrj'  wall,  the  transmission  from  surface 
to  surface  is  almost  perfect;  but  because  of  the  great  mass  and 
rigidity  of  tlie  wall,  it  takes  uj)  but  little  of  the  vibration  of  the  inci- 
dent sound.  It  is  entirely  possible  to  express  by  a  not  verj'  compli- 
cated analytical  e(|uation  the  amoimt  of  soimd  which  a  wall  of 
simple  dimensions  will  take  up  and  transmit  in  terms  of  the  mass 
of  the  wall,  its  elasticity,  and  its  viscosity,  and  the  frequency  of 
vibration  of  the  sound.  But  such  an  equation,  while  of  possible 
interest  to  physicists  as  an  exercise,  is  of  no  interest  whatever  to 
architects  because  of  the  difficulty  of  detennining  the  necessary 
coefficients. 

In  the  case  of  multiple  screen  walls,  the  conununication  from 
wall  to  wall,  through  the  intermediate  air  space  or  around  the  edges, 
is  poor  compared  with  the  face  to  face  connuunication  of  a  solid 
wall.  But  the  vibration  of  the  screen  wall  exposed  to  the  sound,  the 
initial  stej)  in  the  process  of  transmission,  is  greatly  enhanced  by  its 
light  and  flexible  character.  Similarly  its  counterpart,  the  .screen 
wall,  which  by  its  vibration  connnunicates  the  sound  to  the  receiv- 
ing room,  is  light,  flexible,  and  responsive  to  relatively  small  forces. 
That  this  responsiveness  of  tin-  walls  compensates  or  more  than 
compensates  for  the  poor  communication  between  them,  is  the 
probable  explanation  of  the  transmission  betwetii  tlu-  rooms  in  the 
New  England  Conservatory. 

The  Institute  of  Musical  Art  in  New  York  presented  interesting 
variations  of  the  problem.  Here  al.so  the  rooms  on  the  second  and 
third  floors  were  intended  for  private  instruction  and  were  designed 
to  be  sound  proof  from  each  other,  from  the  corridor,  and  from  the 
rooms  above  and  below.  The  walls  sejjarating  the  rooms  from  the 
corridors  were  double,  having  connection  only  at  the  door  jambs 
and  at  the  floor.     The  screen  wall  lu-xt   llie  corridor  was  of  terra 


240 


THE  INSULATION  OF  SOLTND 


cotta  block,  fiiiislied  on  tlie  corridor  side  with  plaster  applied  directly 
to  the  terra  cotta.  The  wall  next  the  room  was  of  gj-psum  block, 
plastered  and  finished  in  burlap.  In  the  air  space  between  the  two 
walls,  deadening  sheet  was  hung.  The  walls  separating  the  rooms 
were  of  gA'psum  block  and  finished  in  hard  plaster  and  burlap.  As 
siiown  on  the   diagram    (Fig.   1),   these   walls   were  cellular,  one 


SECTION  TKROCOBBIDOli 
PA(5TlTION    WALL 


Fig.  1.     Details  of  Construction,  Institute  of  Musical  Art, 
New  York,  N.  Y. 


of  these  cells  being  entirely  enclosed  in  gypsum  block,  the  others 
being  closets  opening  the  one  to  one  room,  the  other  to  the  other. 
The  closets  were  lined  with  wood  sheathing  which  was  separated 
from  the  enclosing  wall  by  a  narrow  space  in  which  deadening  sheet 
was  himg  in  double  thickness  with  overlapping  joints.  In  the  en- 
tirely enclosed  cell,  deadening  sheet  was  also  hung  in  double  thick- 


ness. 


THE  INSULATION  OF  SOUND  241 

It  is  not  difficult  to  see,  at  least  after  the  fact,  why  the  deadening 
sheet  in  such  positions  was  entirely  without  effect.  The  transverse 
masonry  webs  afforded  a  direct  transmission  from  side  to  side  of  the 
compound  wall  that  entirely  overwhelmed  the  transmission  through 
the  air  spaces.  Had  there  been  no  necessity  of  closets,  and  therefore, 
no  necessity  of  transverse  web  and  had  the  two  screen  walls  been 
truly  insulated  the  one  from  the  other,  not  merely  over  their  area, 
but  at  the  floor,  at  the  ceiling,  and  at  the  edges,  the  insulation  would 
have  been  much  more  nearly  perfect. 

The  means  which  were  taken  to  secure  insulation  at  the  base  of 
the  screen  walls  and  to  prevent  the  transmission  of  sound  from  floor 
to  floor  are  exceedingly  interesting.  The  floor  construction  con- 
sisted in  hollow  terra  cotta  tile  arches,  on  top  of  this  cinder  concrete, 
on  this  sawdust  mortar,  and  on  the  top  of  this  cork  flooring.  Below 
the  reenforced  concrete  arches  were  hung  ceilings  of  plaster  on  wire 
lath.  This  hung  ceiling  was  supported  by  crossed  angle  bars  which 
were  themselves  supported  by  the  I  b«>ams  which  supported  the 
hollow  terra  cotta  tile  arches.  In  the  air  spaces  between  the  tile 
arches  and  the  hung  ceilings,  and  resting  on  the  latter,  was  deaden- 
ing sheet.  This  compound  floor  of  cork,  sawdust  mortar,  cinder 
concrete,  terra  cotta  tile,  air  space,  and  lumg  ( ciliiig,  with  deadening 
sheet  in  the  air  spaces,  has  the  air  of  finality,  but  was  not  successful 
in  securing  the  desired  insulation. 

It  is  interesting  to  note  also  that  the  screen  walls  were  separated 
from  the  floor  arches  on  which  they  rested  below  and  on  which  they 
abutted  above  by  deadening  sheet.  It  is  possible  that  this  afforded 
some  insulation  at  the  top  of  the  wall,  for  the  arch  was  not  sustained 
by  the  wall,  and  the  pressure  at  that  point  not  great.  At  the  bottom, 
however,  it  is  improbable  tiial  the  deadening  sheet  carried  under  the 
base  offered  an  insulation  of  practical  value.  Under  the  weight  of 
the  wall  it  was  probably  compressed  into  a  compact  mass,  whose 
rigidity  was  still  furtlier  increased  by  the  percolation  through  it  of 
the  cement  from  the  surroinidiiig  concrete- 
Finally,  after  the  completion  of  the  building,  Mr.  Damrosch,  the 
director,  had  tried  the  cxpfriiiu-nt  of  covering  tlie  walls  of  one  of  the 
rooms  to  a  depth  of  two  inches  with  slandanl  hair  felt,  with  some, 
but  almost  negligible,  effect  on  tlie  transmission  of  sound. 


242  THE  INSriATIOX  OF  SOUND 

Deadoninj,'  slu'ct  has  been  mentioned  frequently.  All  indication 
of  the  special  kind  employed  has  been  purposely  omitted,  for  the 
discussion  is  concerned  with  the  larger  question  of  the  manner  of  its 
use  and  not  with  the  relative  merits  of  the  different  makes. 

The  house  in  New  York  presented  a  problem  even  more  interest- 
ing. It  was  practically  a  double  house,  one  of  the  most  imperative 
conditions  of  the  building  being  the  exclusion  of  sounds  in  the  main 
part  of  the  hou.se  from  the  part  to  the  left  of  a  great  partition  wall. 
This  wall  of  solid  ma.sonrj'  .supported  only  one  beam  of  the  main 
house,  was  pierced  by  as  few  doors  as  possible  —  two  —  and  by 
no  steam  or  water  pipes.  The  rooms  were  heated  by  independent 
fireplaces.  The  water  pipes  connected  independently  to  the  main. 
It  had  been  regarded  as  of  particular  importance  to  exclude  .sounds 
from  the  two  bedrooms  on  the  second  floor.  The  ceilings  of  the 
rooms  below  were,  therefore,  made  of  concrete  arch;  on  top  of  this 
was  spread  three  inches  of  sand,  and  on  top  of  this  three  inches  of 
lignolith  blocks;  on  this  was  laid  a  hardwood  floor;  and  finally, 
when  the  room  was  occupied,  this  floor  was  covered  by  very  heavy 
and  heavily  padded  carpets.  From  the  complex  floor  thus  con- 
structed arose  interior  walls  of  plaster  on  wire  lath  on  independent 
studding,  supported  only  at  the  top  where  they  were  held  from  the 
masonr^'  walls  by  iron  brackets  set  in  lignolith  blocks.  Each  room 
was,  therefore,  practically  a  room  within  a  room,  separated  below 
by  three  inches  of  sand  and  three  inches  of  lignolith  and  on  all  sides 
and  above  by  an  air  space.  Notwithstanding  this,  the  shutting  of  a 
door  in  any  part  of  the  main  house  could  be  heard,  though  faintly, 
in  either  bedroom.  In  the  rear  bedroom,  from  which  the  best  results 
were  expected,  one  could  hear  not  merely  the  shutting  of  doors  in 
the  main  part  of  the  house,  but  the  working  of  the  feed  pump,  the 
raking  of  the  furnace,  and  the  coaling  of  the  kitchen  range.  In  the 
basement  of  the  main  dwelling  was  the  servants'  dining  room.  Rap- 
ping with  the  knuckles  on  the  wall  of  this  room  produced  in  the  bed- 
room, two  stories  up  and  on  the  other  side  of  the  great  partition  wall, 
a  sound  which,  although  hardly,  as  the  architect  expressed  it,  magni- 
fied, yet  of  astonishing  loudness  and  clearness.  In  this  case,  the 
telephone-like  nature  of  the  process  was  even  more  clearly  defined 
than  in  the  other  cases,  for  the  distances  concerned  were  much 


THE  INSULATION  OF  SOUND  243 

greuttT.  The  problem  had  many  interesting  aspects,  but  will  best 
serve  the  present  purpose  if  for  the  sake  of  simplicity  and  clearness 
it  be  held  to  but  one,  —  the  transmission  of  sound  from  the  servants' 
dining  room  in  the  basement  along  the  great  eighteen-inch  partition 
wall  up  two  stories  to  the  insulated  bedroom  above  and  opposite. 

It  is  a  fairly  safe  hazard  that  the  sound  on  reaching  the  bedroom 
did  not  ciih  r  l)y  way  ol'  tlic  floor,  lor  I  lie  combination  of  reenforced 
concrete,  three  inches  of  sand,  three  inches  of  lignolith  block,  and 
the  wood  flooring  and  carpet  above,  presented  a  combination  of 
massive  rigidity  in  the  concrete  arch,  inertness  in  the  sand  and 
lignolith  block,  imperviousness  in  the  hardwood  floor,  and  absorp- 
tion in  llic  padded  carpet  which  rendered  insulation  pcrlVct,  if  ])er- 
fect  insulation  be  possible.  No  air  ducts  or  steam  or  water  ])ipes 
entered  the  room.  The  only  conceivable  conununication,  therefore, 
was  through  the  walls  or  ceiling.  The  comnumication  to  the  inner 
walls  and  ceiling  from  the  surrounding  structural  walls  was  either 
through  the  air  sjjace  or  through  the  iron  angle  bars,  which,  set  in 
lignolith  blocks  in  the  structural  wall,  retained  erect  and  at  proper 
ilistancf  the  inner  walls.  Of  the  two  nu'ans  of  comnumication,  the 
air  and  the  angle  bars,  the  latter  was  probably  the  more  important. 
It  is  interesting  and  pertinent  to  follow  this  line  of  comnumication, 
the  masonrv'  wall,  the  angle  bars,  and  the  screen  walls,  and  to  en- 
deavor to  discover  if  possible,  or  at  least  to  speculate  on  the  reason 
for  its  exceptional  though  unwelcome  efficiency. 

From  the  outset  it  is  necessarj'  to  distinguish  the  transverse  and 
the  longitudinal  transmission  of  .sound  in  a  building  member,  that 
is.  to  distinguish  as  somewhat  ditt'erent  processes  the  transmission 
of  sound  from  one  room  to  an  adjacent  room  through  a  se])arating 
wall  or  ceiling,  fnnu  I  lie  liaiisTiiissioM  of  sound  along  tiie  floors  from 
room  to  room,  or  along  the  xcrl  ical  walls  from  floor  to  floor.  liroadly, 
although  the  two  are  not  entirely  separable  |)lienomena,  t)ne  is 
largel\'  concerneil  in  the  transmission  of  the  .sound  of  the  voice,  or 
the  violin,  or  of  other  .sources  free  from  .solid  contact  with  the  floor, 
anil  I  lie  ot  her  in  I  lie  t  raiismission  of  t  he  >ouii<l  of  a  i)iano  or  cello  in- 
struments in  direct  comnumication  with  the  JMiilding  structure — or 
of  noi.ses  involved  in  the  oi)erat  ion  of  the  i)uil(ling,  dynamos,  eleva- 
tors, or  the  opening  and  i-losiiig  of  doors.    In  the  building  under  con- 


244  thp:  insulation  of  SOUNT) 

siileriition.  the  disturbing  sounds  were  in  everj'  case  communicated 
directly  to  the  struclure  at  a  considerable  distance  and  transmitted 
along  the  walls  until  ultimately  communicated  through  the  angle 
bars,  if  the  angle  bars  were  the  means  of  commimication,  to  the  thin 
plaster  walls  which  constituted  the  inner  room.  The  special  features 
thus  emphasized  were  the  longitudinal  transmission  of  vibration  by 
walls,  floors,  and  structural  beams,  and  the  transformation  of  these 
longitudinal  vibrations  into  the  sound-producing  transverse  vibra- 
tions of  walls  and  ceilings  boimding  the  disturbed  room.  Many 
questions  were  raised  which  at  the  time  could  be  only  tentatively 
answered. 

What  manner  of  walls  conduct  the  sound  with  the  greater  readi- 
ness ?  Is  it  true,  as  so  often  stated,  that  modern  concrete  construc- 
tion has  contributed  to  the  recent  prevalence  of  these  difficulties  .'' 
If  so,  is  there  a  difference  in  this  respect  between  stone,  sand,  and 
cinder  concrete  ?  In  this  particular  building,  the  partition  wall  was 
of  brick.  Is  there  a  difference  due  to  the  kind  of  brick  employed, 
whether  hard  or  soft  ?  Or  does  the  conduction  of  sound  depend  on 
the  kind  of  mortar  with  which  the  masonrj'  is  set  ?  If  this  seems 
trivial,  consider  the  number  of  joints  in  even  a  moderate  distance. 
Again,  is  it  possible  that  sound  may  be  transmitted  along  a  wall 
without  producing  a  transverse  vibration,  thus  not  entering  the 
adjacent  room  ?  Is  it  possible  that  in  the  case  of  this  private  house 
had  there  been  no  interior  screen  wall  the  sound  communicated  to 
the  room  would  have  been  less  ?  We  know  that  if  the  string  of  a 
string  telephone  passes  through  a  room  without  touching,  a  conver- 
sation held  over  the  line  will  be  entirely  inaudible  in  the  room.  Is 
it  possible  that  something  like  this,  but  on  a  grand  scale,  may  happen 
in  a  building  .''  Or,  again,  is  it  possible  that  the  iron  brackets  which 
connected  the  great  partition  wall  to  the  screen  wall  magnified  the 
motion  and  so  the  sound,  as  the  lever  on  a  phonograph  magnifies  its 
motion  ?  These  are  not  unworthy  questions,  even  if  ultimately  the 
answer  be  negative. 

The  investigation  divides  itself  into  two  parts,  —  the  one  dealing 
with  partition  walls  especially  constructed  for  the  test,  the  other 
with  existing  structures  wherever  found  in  interesting  form.  The 
experiments  of  the  former  type  were  conducted  in  a  special  room. 


THE  INSULATION  OF  SOUND 


245 


mentioned  in  some  of  tlie  earlier  papers  (The  Brickbuilder,  January, 
1914),'  and  having  peculiar  merits  for  the  work.  For  an  imder- 
standing  of  these  experiments  and  an  appreciation  of  the  conditions 
that  make  for  their  accuracy,  it  is  necessan,'  that  the  construction  of 
this  room  be  explained  at  some  length.  The  west  wing  of  the  Jeffer- 
son Physical  Laboratory  is  in  plan  a  large  square  in  the  center  of 
which  rises  a  tower,  which,  for  the  sake  of  steadiness  and  insulation 


Fig.  i.     Ti'sting  Room  anil  Aiiparatus 

from  all  external  vil)rati<)n,  is  not  merely  of  indepentlent  walls  but 
has  an  entirely  se])arate  foundation,  and  above  is  spanned  without 
touching  by  the  roof  of  the  main  building.  The  sub-basement  room 
of  this  tower  is  below  the  basement  of  the  main  building,  but  the 
walls  of  the  latter  are  carried  down  to  enclose  it.  The  floor  of  the 
room  is  t)f  concrete,  the  ceiling  a  masonry  arch.  There  is  but  one 
door  which  leads  through  a  small  anteroom  to  the  stairs  mounting 
to  the  1<'\-<'1  <if  I  lie  l)asemenl   of  tiic  main  building.    Through  the 

'  See  page  1!>U,  chapter  8. 


24G  THE  INSULATION  OF  SOUND 

ceilinjj  llu're  arc  two  small  openings  for  which  special  means  of  closing 
are  provided.  The  larger  of  these  openings  barely  permits  the 
passage  of  an  observer  when  raised  or  lowered  by  a  block  and  tackle. 
It  is  necessary  that  there  be  some  such  entrance  in  order  that  obser- 
vations may  be  taken  in  the  room  when  the  door  is  closed  by  the  wall 
construction  undergoing  test. 

Of  i)rime  importance,  critical  to  the  whole  investigation,  was  the 
insulation  between  the  rooms,  otherwise  than  through  the  partition 
to  be  tested.  The  latter  closed  the  doorway.  Other  than  that  the 
two  rooms  were  separated  by  two  eigliteen-inch  walls  of  brick, 
separated  by  a  one-inch  air  space,  not  touching  through  a  five-story 
height  and  carried  down  to  separate  foimdations.  Around  the  outer 
wall  and  around  the  antechamber  was  solid  ground.  It  is  difficult 
to  conceive  of  two  adjacent  rooms  better  insulated,  the  one  from 
the  other,  in  all  directions,  except  in  that  of  their  immediate  con- 
nection. 

The  arrangement  of  apparatus,  changed  somewhat  in  later  experi- 
ments, consisted  primarily,  as  shown  in  the  diagram,  of  a  set  of 
organ  pipes,  winded  from  a  bellows  reservoir  in  the  room  above, 
this  in  turn  being  charged  from  an  air  pump  in  a  remote  part  of  the 
building,  —  remote  to  avoid  the  noise  of  operation.  In  the  center 
of  the  room  two  reflectors  revolved  slowly  and  noiselessly  on  roller 
bearings,  turned  continuously  by  a  weight,  under  governor  control, 
in  the  room  above.  The  chair  of  the  observer  was  in  a  box  whose 
folding  lids  fitted  over  his  shoulders.  In  the  box  was  the  small  organ 
console  and  the  key  of  the  chronograph.  The  organ  and  chrono- 
graph had  also  console  and  key  connection  with  the  antechamber. 
The  details  of  the  apparatus  are  not  of  moment  in  a  paper  written 
primarily  for  architects. 

Broadly,  the  method  of  measuring  the  transmission  of  sound 
through  the  partitions  consisted  in  producing  in  the  larger  room  a 
sound  whose  intensity  in  terms  of  threshold  audibility  was  known, 
and  reducing  this  intensity  at  a  determinable  rate  until  the  soimd 
ceased  to  be  audible  on  the  other  side  of  the  partition.  The  intensity 
of  the  sound  at  this  instant  was  nimierically  equal  to  the  reciprocal 
of  the  coefiicient  of  transmission.  This  process  involved  several 
considerations  which  should  at  least  be  mentioned. 


THE  INSULATIOX  OF  SOl^'D  247 

The  souiul  of  known  inlt-nsity  was  producctl  l)y  organ  pipes  of 
know-n  powers  of  emission,  allowance  being  made  for  the  vohnne  of 
the  room,  and  tlie  absorbing  ])OW('r  of  the  walls.  'I'lic  inclliod  was 
fully  explained  in  earlier  papers.'  It  is  to  be  borne  in  mind  that 
there  was  thus  determined  merely  the  average  of  intensity.  The 
intensity  varied  greatly  in  diil'ercnt  ])arts  of  tlie  room  because  of 
interference.  In  order  that  the  average  intensity  of  sound  against 
the  partition  in  a  series  of  observations  should  e((vial  the  average 
intensity  in  the  room,  it  was  necessary  to  continuously  shift  the  in- 
terference system.  This  was  accomplished  by  means  of  revolving 
reflectors.  This  also  rendered  it  possible  to  obtain  a  measure  of 
average  conditions  in  the  room  from  observations  taken  in  one 
position.  Finally  the  observations  in  the  room  were  always  made 
by  the  observer  seated  in  the  box.  as  this  rendered  his  clothing  a 
negligil)le  factor,  and  the  condition  of  the  room  the  same  wuth  or 
without  his  presence.  Consideration  was  also  given  to  the  acoustical 
condition  of  llic  anlcchaiiibtT. 

Two  methods  of  reducing  the  sound  have  l)een  employed.  In 
the  one  the  sound  was  allowed  to  die  away  naturally,  the  source 
being  stopped  suddenly,  and  the  rate  at  which  it  decreased  deter- 
mined from  the  constants  of  tlic  room.  In  another  type  of  experi- 
ment the  source,  electrically  maintained,  was  reduced  by  the  addition 
of  electrical  resistance  to  the  circuit.  One  method  was  sviitable 
to  one  set  of  contlitions,  the  other  to  another.  The  first  was  em- 
ployed in  the  experiments  whose  residts  are  given  in  tliis  jjajxr. 

The  first  measurements  were  on  felt,  partly  suggested  by  the  ex- 
periments of  Dr.  Damrosch  with  felt  on  the  walls  of  the  Institute  of 
Musical  Art,  partly  ijecause  it  offered  the  tlynanucally  simplest  jjrob- 
lem  on  which  to  test  the  accuracy  of  the  method  by  the  concurrence 
of  its  results.  The  felt  u.sed  was  that  so  thoroughly  studied  in  other 
acoustical  asjjecls  in  the  i)aper  i)ublished  in  the  Proceedings  of  the 
American  Academy  of  Arts  and  Scii-nces  in  liXMi.  The  tloor  separat- 
ing the  two  rooms  was  covered  with  a  one-half  inch  thickness  of  this 
fell,  i'lic  inlinsity  of  sounil  in  I  lie  main  room  just  audible  through 
the  fell  was  .'{.7  times  threshold  audibility.  Aiitither  layer  of  felt 
of  equal  thickness  was  added  to  the  fii>t,  and  the  reduction  in  the 

'See  liiviTKcriition.  pap'  1. 


"248 


THE  INSULATION  OF  SOUND 


intensity  of  sound  in  i)iissing  throngli  tlie  two  was  7.8  fold.  Tlirough 
three-thickness,  each  one-half,  the  reduction  was  15.4  fold,  through 
four  30.4,  five  47.5,  and  six  88.0.  This  test  was  for  sounds  having  the 
pitch  of  violin  C,  first  C  above  middle  C,  512  vibrations  per  second. 
There  is  another  way  of  stating  the  above  results  which  is  perhaps 
of  more  service  to  architects.     The  ordinary  speaking  intensity  of 

10 


.8 


.6 


\ 

\l 

\ 

k 

3 

,2^ 

"-^ 

^~ 

1 

12  3  4  6  6 

Fig.  3 

the  voice  is  —  not  exactly,  of  course,  for  it  varies  greatly  —  but 
of  the  order  of  magnitude  of  1,000,000  times  minimum  audible  in- 
tensity. Assimie  that  there  is  a  sound  of  that  intensity,  and  of  the 
pitch  investigated,  in  a  room  in  one  side  of  a  partition  of  half-inch 
felt.  Its  intensity  on  the  other  side  of  the  partition  would  be 
270,000  times  minimum  audible  intensity.    Through  an  inch  of  felt 


THE  INSl  LATIOX  OF  SOUND  ^240 

ils  intensity  would  be  128,000.  Through  six  hiyers  of  sucli  fVlt,  that 
is,  through  three  inches,  its  intensity  would  be  11,400  times  mini- 
mum audible  intensity,  —  very  audible,  indeed.  The  diminishing 
intensity  of  the  sound  as  it  proceeds  through  layer  after  layer  of 
felt  is  plotted  in  the  diagram  (Curve  1,  Fig.  3),  in  which  all  the 
points  recorded  are  the  direct  results  of  observations.  The  intensity 
inside  the  room  is  the  full  ordinate  of  the  diagram.  The  curve  drawn 
is  the  nearest  rectangular  hyperbola  fitting  the  observed  and  calcu- 
lated points.  The  significance  of  this  will  be  discus.sed  later.  It  is 
sufficient  for  the  present  i)uri)ose  to  say  that  it  is  the  theoretical 
curve  for  these  conditions,  and  the  close  agreement  between  it  and 
the  observed  points  is  a  matter  for  considerable  satisfaction. 

The  next  partition  tested  was  of  sheet  iron.  This,  of  course,  is 
not  a  normal  building  nuiti'rial  and  it  may  therefore  seem  disap- 
])ointing  and  without  interest  to  architects.  But  it  is  necessar}'  to 
remember  that  these  were  preliminarj'  investigations  establishing 
methods  and  principles  rather  than  practical  data.  Moreover,  the 
material  is  not  wholly  impractical.  The  writer  has  used  it  in  recom- 
mendations to  an  architect  in  one  of  tlK>  most  interesting  and  suc- 
cessful cases  of  sound  insidation  .so  far  underlaktii  tliat  in  an 
after-theatre  restaurant  extending  imderneal  li  t  lie  sidewalk  of  Broad- 
way and  42d  Street  in  New  York. 

The  successive  layers  of  sheet  iron  were  held  at  a  distance,  each 
from  the  preceding,  of  one  inch,  spaced  at  the  edges  by  a  narrow 
strip  of  wood  and  felt,  and  pressed  home  by  washers  of  felt.  After 
the  practical  cases  cited  at  the  beginning  of  the  paper,  it  requires 
courage  and  some  hardihood  to  say  that  any  insulation  is  good.  It 
can  only  be  said  thai  every  care  was  taken  to  this  end.  The  results 
of  the  experiments  can  alone  measure  Hie  <fliciency  of  the  inetlK.ii 
employed,  and  later  they  will  be  discussed  with  this  in  view. 

The  third  series  of  exi)eriments  were  with  layers  of  slun-t  iron 
with  one-half  inch  felt  occu])yiug  part  of  the  air  space  U-tweeii  theni. 
The  iron  was  that  used  in  the  second  series,  the  fell  that  u.s«'d  in  the 
first.  The  air  space  was  unfortunately  slightly  greater  tliau  in  the 
second  series,  being  an  inch  and  a  (|uarler  instead  of  an  incli.  The 
magnitude  of  the  effect  of  this  ditVerence  in  distance  was  not 
realized  at  the  time,  but  it  was  sufhcienl  to  prevent  a  direct  com- 


>.-,0  THE  INSULATION  OF  SOUND 

parisou  of  the  second  and  tliirtl  scries,  and  an  attempt  to  deduce 
the  latter  from  the  former  witli  the  aid  of  the  first.  When  this  was 
realized,  other  conditions  were  so  different  as  to  make  a  repetition 
of  the  series  difficuU. 

In  the  foUowinff  tahle  is  given  the  results  of  these  three  series  of 
experiments  in  such  form  as  to  admit  of  easy  comparison.  To  tliis 
end  they  are  all  reduced  to  the  values  which  they  would  have  had 
with  an  intensity  of  sound  in  the  inner  room  of  1,000,000.  In  the 
first  column  each  succeeding  figure  is  the  intensity  outside  an  addi- 
tional half  inch  of  felt.  In  the  second  column,  similarly,  each  suc- 
ceeding figure  is  the  intensity  outside  an  additional  sheet  of  iron. 
In  the  third  column,  the  second  figure  is  the  intensity  outside  a 
single  sheet  of  iron,  and  after  that  each  succeeding  figure  is  the 
intensity  outside  of  an  additional  felt  and  iron  doublet  with  air  space. 


1,000.000 

1,000,000 

1.000,000 

'270,000 

22,700 

23,000 

1'28,000 

8,700 

3,300 

65,000 

4,880 

700 

33,000 

3,150 

220 

21,500 

2,000 

150 

11,400 

1,520 

88 

The  sound  transmitted  in  the  second  and  third  series  is  so  much 
less  than  in  the  first  that  when  an  attempt  is  made  to  plot  it  on  the 
same  diagram  (Curves  2  and  3,  Fig.  3)  it  results  in  lines  so  low  as  to 
be  scarcely  distinguishable  from  the  base  line.  ^Magnifying  the  scale 
tenfold  (Fig.  4)  throws  the  first  series  off  the  diagram  for  the  earlier 
values,  but  renders  visible  the  second  and  third. 

The  method  of  representing  the  results  of  an  investigation 
graphically  has  several  ends  in  view :  it  gives  a  visual  impression  of 
the  phenomenon;  it  shows  by  the  nearness  with  which  the  plotted 
values^  lie  to  a  smooth  curve  the  accuracy  of  the  method  and  of  the 
work;  it  serves  to  interpolate  for  intermediate  values  and  to  ex- 
trapolate for  points  which  lie  beyond  the  observed  region,  forward 
or  backward;   finally,  it  reveals  significant  relations  and  leads  to  a 

'  In  reproducing  from  the  plotted  diagrams  for  Figs.  3,  4,  and  5,  the  dots,  in  some  cases, 
wliich  indicated  the  plotted  values  of  the  observed  points,  do  not  clearly  appear  in  distinction 
on  the  lines.  The  greatest  divergence,  in  any  case,  from  the  line  drawn  was  not  more  than 
twice  the  breadth  of  the  lire  itself. 


THE  IXST'LATIOX  OF  SOI  XD 


251 


more  effective  discussion.     It  is  worth  wliile  thus  examining  the 
three  curves. 

Attention  has  already  been  called  to  the  curve  for  felt,  to  its  ex- 
trapolation, and  to  the  close  approximation  of  the  observed  points 
to  an  hyperbola.    The  latter  fact  indicates  the  sinii)lest  possible  law 

10 


.09 
.08 
.07 
.06 
.06 
.04 
.03 
.02 
.01 


12  3  4  6  6 

Fiii.  I 

of  aliMirplioii.  Il  |)ro\(s  llml  :ill  l:iyci>  aliM)il>  III.'  -niiir  |>n>pt>rt ion 
(iT  llic  .soiuid;  llial  cacli  succeeding  layer  al).sorl)s  le.s.s  actual  .»(>un<l 
liian  tile  prcccdiug.  l)ut  less  merely  because  Ic.vs  .souiiil  reaches  it  to 
be  absorbed.  In  the  ca.se  in  hand  the  .souiul  in  pa.vMug  through  the 
felt  was  reduced  in  the  ratio  1.S8  in  each  layer.  :t.."):{  in  .ach  ukIi. 
It  is  customary  to  tot  >U(li  curvo  by  plotting  them  on  a  .siH-«ial 
kiiiii   of  coordinate  i)aper.        <>iw  «>n   whirh,   while    horizontal   <li>- 


\  1 

\ 

\ 

\ 

w 

\ 

l~ — — t-.. 

1 

<2.n  THE  INSULATION  OF  SOUND 

tancc's  are  iinifonnly  scaled  as  before,  vertical  distances  are  scaled 
with  jjreater  and  greater  reduction,  tenfold  for  each  unit  rise.  On 
such  coordinate  paper  the  vertical  distances  are  the  power  to  which 
10  must  be  raised  to  equal  the  number  plotted  —  in  other  words,  it 
is  the  logarithm  of  the  number.    Plotted  on  such  paper  the  curve  for 

10 


10 


10 


10 


10 


10 


10 


10' 


10 


10 


A 

'"---. 

^^ 

^ 

v^ 

"^ 

.^ 

\^ 

2 

, 

> 

"^^3 

2  3 

Fig.  5 


felt  will  result  in  a  straight  line,  if  the  curve  in  the  other  diagram 
was  an  hyperbola,  and  if  the  law  of  absorption  was  as  inferred.  How 
accurately  it  does  so  is  shown  in  Curve  1,  Fig.  5. 

^^  hen  the  ob.servations  for  iron,  and  for  felt  and  iron,  are  similarly 
plotted  (Curves  2  and  3,  Fig.  5),  the  lines  are  not  straight,  but 
strongly  curved  upward,  indicating  that  the  corresponding  curves 
in  the  preceding  diagram  were  not  hyperbolas,  and  that  the  law  of 


THE  INSULATION  OF  SOLTND  253 

constant  coefficient  did  not  hold.  This  must  be  explained  in  one  or 
the  other  of  two  ways.  Either  there  was  some  by-pass  for  the  sound, 
or  the  efficiency  of  each  succeeding  unit  of  construction  was  less. 

The  by-pass  as  a  possible  explanation  can  be  c|uickly  disposed  of. 
Take,  for  example,  the  extreme  case,  that  for  fell  luid  iron,  and  make 
the  extreme  assumption  that  with  the  completed  series  of  six  screens 
all  the  sound  has  come  by  some  by-pass,  the  surrounding  walls,  the 
foundations,  the  ceiling,  or  by  some  solid  connection  from  the  inner- 
most to  the  outermost  sheet.  A  calculation  based  on  these  assmnp- 
tions  gives  a  plot  whose  curvature  is  entirely  at  the  lower  end  and 
bears  no  relationship  to  the  observed  values.  In  t  hr  ot  lier  case,  that 
of  the  iron  only,  a  similar  calcidation  gives  a  similar  result;  more- 
over, the  much  lower  limit  to  which  the  felt  and  iron  screens  reduci>d 
the  sound  wholly  eliminates  any  by-pa.ss  action  as  a  vital  factor  in 
the  iron-only  experiment. 

The  other  explanation  is  not  merely  necessary  bj'  elimination, 
but  is  dynamically  rational.  'J'iie  screen  walls  such  as  here  tested, 
as  well  as  the  screen  walls  in  the  actual  construction  described  by 
way  of  introduction,  do  not  act  by  absorption,  as  in  the  ca.se  of  the 
felt;  <lo  not  act  by  a  process  which  is  complete  al  the  jxiiiil.  but 
rather  by  a  process  which  in  the  first  screen  may  be  likened  to  re- 
flection, and  in  the  second  and  subsequent  screens  by  a  jirocess  which 
nuiy  be  more  or  le.ss  likened  to  reflection,  but  which  being  in  a  con- 
fined space  reacts  on  the  screen  or  screens  wliich  lia\c  i)r(((<l<il  it. 
In  fact,  the  process  nuist  be  regarded  not  as  a  sequence  of  inde- 
pendent steps  or  a  j)rogre.ss  of  an  independent  action,  but  as  that  of 
a  structure  wliicli  must  be  considered  dynamieally  as  a  whole. 

When  I  lie  phenomenon  is  one  of  i)ure  ab.sorplion.  as  in  felt,  it  is 
possible  to  express  by  a  sim])le  fornuiia  the  intensity  of  tin-  ><>iin<l  1, 
at  any  distance  x,  in  terms  of  the  inilial  inleiisily  1„, 

I  =  I„Rk% 

where  11  represents  I  lie  factor  of  surface  discoiil  iiiuil\-.  and  k  the 
ratio  in  which  the  intensity  is  reduced  in  a  unit  distance.  In  the  ea.se 
of  the  felt  tested,  R  is  AHr>  and  k  is  :5.j:?,  the  distance  into  tlie 
felt  being  measiin'd  in  inches.  .\s  an  ai)|)lication  of  tiiis  f..rnuda. 
one  nuiy  compute  tlie  tliiekne.ss  of  fell    wliieh   wouM  entirely  ex- 


'2.54  THE  INSULATION  OF  SOUND 

tin^iiisli  ii  .soiincl  of  llic  iiilcnsiU-  of  oriliiiiiry  speech, —  10. 4  inches. 
It  is  not  possible  to  express  by  sucli  a  forniiihi  the  transmission  of 
sound  through  either  of  tlie  more  complex  structures.  However,  it 
is  possible  to  e.xtrapolate  empirically  and  show  that  10.4  inches  of 
neither  would  accomplish  this  ideal  residt.  although  they  are  both 
far  superior  to  felt  lor  thicknesses  up  to  three  inches  in  one  case  and 
five  and  one-half  inches  in  the  other. 

A  number  of  other  experiments  were  tried  during  this  preliminary 
stage  of  the  investigation,  such,  for  example,  as  increasing  the 
distance  between  the  screen  walls,  but  it  is  not  necessary  to  recount 
them  here.  Enough  has  already  been  given  to  show  that  a  method 
had  been  developed  for  accurately  measuring  the  insulating  value  of 
structures;  more  would  but  confuse  the  purpose.  At  this  point  the 
apparatus  was  improved,  the  method  recast,  and  the  investigation 
begun  anew,  thenceforward  to  deal  only  with  standard  forms  of 
construction,  and  for  sounds,  not  of  one  pitch  only,  but  for  the 
whole  range  of  the  musical  scale. 


11 

WHISPERING  GALLERIES 

It  is  probable  that  all  existing  whispering  galleries,  it  is  certain  that 
the  six  more  famous  ones,  are  accidents;  it  is  equally  certain  that  all 
could  have  been  predetermined  without  difficulty,  and  like  most 
accidents  could  have  been  improved  upon.  That  these  six,  the 
Dome  of  St.  Paul's  Cathedral  in  London,  Statuary  Hall  in  the  Capi- 
tol at  Washington,  the  vases  in  the  Salle  des  Cariatides  in  the  Lou\Te 
in  Paris,  St.  John  Lateran  in  Rome,  The  Ear  of  Dionysius  at  Syra- 
cuse, and  the  Catliedral  of  Ciirgenfi,  are  famous  al)ove  others  is  in  a 
measure  due  to  some  incident  of  place  or  association.  Four  are  fa- 
mous because  on  the  great  routes  of  tourist  travel,  one  because  of 
classical  traditions,  and  one,  in  an  exceedingly  inaccessible  city  and 
itself  still  more  inaccessible,  tlu-oufjh  a  curious  story  perjietuated  by 
Sir  Jolin  W.  Herschel  in  the  Encyclopedia  Melropolikuui.  However, 
all  show  the  phenomenon  in  a  striking  numner  and  merit  the  interest 
wliicli  they  excite,  an  interest  probably  enhanced  by  the  mysterj' 
attaching  to  an  unpremeditated  event  in  the  five  more  modern  cases, 
and  none  the  less  enhanced  in  the  other  l)y  the  tradition  of  its  inten- 
tional design  and  as  evidence  of  a  "lost  art." 

The  whispering  gallery  in  the  Capitol  at  Washington  is  of  the 
simplest  possible  type. 

The  Cajjitol  as  first  built  was  but  the  central  i)(>rti()n  of  the  i)resent 
building,  the  Senate  Chamber  and  the  Hail  of  the  IIou.se  of  Repre- 
sentatives being  at  that  time  innnediately  ailjacent  to  the  rotunda. 
With  the  admission  of  new  states,  and  witli  tlic  general  increase  in 
l)opuIation,  the  Senate  and  the  House  outgrew  their  (piarters.  and  in 
ISjI  the  great  wings  which  now  oomiilcte  the  building  were  con- 
structed for  their  acconmiodalion.  Tlir  oM  Hall  of  llic  House,  which 
in  its  day  must  have  been  acoustically  an  exceedingly  p(H)r  assembly 
room,  was  transformed  into  the  jjre.sent  Hall  of  Statues  and  became, 
or  rather  remaiiu-d,  one  of  the  most  perfeet  of  whis])ering  galleries. 

The  ceiling  of  the  Ilall  of  Statues,  with  the  exception  of  a  small 
circular  skylight,  is  a  j)ortion  of  an  exact  sphere  with  its  center  very 

us 


o 

Q 

d 


^ 


a. 
a 


5 

en 


WHISPERING  GALLERIES  257 

nearly  at  head  level.  As  shown  in  the  illustrations  the  ceiling  is  cof- 
fered. As  originally  constructed,  and  as  it  remained  until  1901,  the 
ceiling  was  perfectly  smooth,  being  of  wood,  papered  and  painted  in 
a  manner  to  n>pre.sent  coffering.  In  lf)01,  a  fire  in  the  C'lianiher  of 
the  Supreme  Court,  also  in  the  Capitol,  led  to  a  general  overhauling 
of  the  building,  and  among  other  dangerous  constructions  the  ceiling 
of  wood  in  the  Hall  of  Statues  was  replaced  by  a  fireproof  construc- 
tion of  steel  and  ])laster.  Instead  of  being  merely  painted,  the  new 
ceiling  had  recessed  panels  with  mouldings  and  ribs  in  relief 
(Fig.  1).  In  consequence  of  this  construction,  the  whispering 
gallery  lost  a  large  part  of  its  unique  quality. 

During  the  years  preceding  the  remodeling  of  the  ceiling,  the 
whispering  gallery  had  l)een  of  great  interest  to  toiu-ists  and  deep 
hollows  were  worn  in  the  marble  tile  where  the  observers  stood.  The 
experiment  was  usually  tried  in  either  one  of  two  ways.  The  visitor 
to  the  gallery  was  placed  at  the  center  of  curvature  of  the  ceiling  and 
told  to  whisi)er,  when  the  slightest  sounds  were  returned  to  him 
from  the  ceiling.  The  effect  was  nnich  more  striking  than  one  would 
suppose  from  this  simi)le  description.  The  slight  lapse  of  time  re- 
quired for  the  sound  to  travel  to  tlie  ceiling  and  back,  together  with 
one's  keen  sense  of  direction, gave  the  effect  of  an  invisible  and  mock- 
ing presence.  Or  the  guide  would  ])lace  the  tourists  at  symmetrical 
points  on  either  side  of  the  center,  when  they  could  with  the  lu'l[)  of 
the  ceiling  whisper  to  each  other  across  distances  over  which  they 
could  not  be  heard  directly,  'i'lie  explanation  ol'  this  particular 
whi.sj)ering  gallery  is  exceedingly  simjile. 

Speech,  whether  whispered  or  full  toned,  consists  of  waves  or 
trains  of  waves  of  greatly  \ariecl  character.  The  study,  to  its  la>t 
refinement,  of  whispering  gallery  phenomena  iii\(>l\(s  a  coiisitlera- 
ti(»ii  ('f  this  complicated  character  ol'  .-.pcccli.  luil  a  rough  study,  and 
one  which  serves  most  ])urp()ses,  can  be  made  l)y  following  the  path 
and  the  transformation  of  a  single  wave.  This  can  be  illustrated  l)y 
two  series  of  i)h()fograi)hs.  In  the  one  (Fig.  2),  the  wave  is  .shown  in 
tiie  (litfennt  stages  of  il>  advaiKc  oulwanl.  -  si)lierieal,  exeej)! 
where  it  strikes  the  floor,  the  wall,  or  the  repressed  transverse  arch 
of  the  ceiling.  In  the  second  series  of  pholograpiis  (Fig.  .T).  the 
wave  has  struck  the  si.-hericai  ceiling  everywhere  at  the  same  instant. 


□□ 


WIIISPERIXG  GALLERIES  259 

and,  reversed  in  direction,  gains  in  intensity  as  it  gathers  together 
toward  tlie  point  from  which  it  issued.  The  sound  reflected  from 
the  otlier  surfaces  may  be  seen  dividing  and  subdividing  in  multiple 
reflection  and  losing  in  intensity,  while  the  sound  reflected  from  the 
spherical  ceiling  gains  througli  its  rapid  convergence. 

These  and  other  similar  photographs  used  in  this  investigation 
were  taken  in  a  small  sectional  model,  one-sixteenth  of  an  inch  to 
the  foot  in  scale,  made  of  ))laster  of  Paris  or  of  other  convenient  ma- 
terial, and  the  impulsive  report  or  wave  was  produced  either  by  the 
explosion  of  fulminate  of  mercury  or  directly  l)y  an  electric  spark. 
The  flash  bj*  which  the  exposure  was  taken  had  a  duratioM  of  less 
than  a  millionth  of  a  second.  It  is  wholly  unnecessary  for  the  pur- 
poses of  this  present  discussion  to  go  into  the  details  of  this  process. 
It  is  sufficient  to  state  that  the  illustrations  are  actual  jihotographs 
of  real  souiid-wa\('s  in  I  lie  air  and  reproduce  not  iiu  rely  (he  main 
but  the  subordinate  phenomena. 

Inciting  this  gallery  in  an  article  on  Whis])enng  (Jalleries  in  Stur- 
gis'  Dictionarij  of  Architecture,  the  writer  made  the  statement  that 
"The  ceiling,  painted  so  that  it  appears  deejily  panelled,  is  smooth. 
Had  the  ceiling  been  panelled  the  reflection  would  have  been  irregu- 
lar and  the  effect  very  much  reduced."  A  year  or  so  after  this  was 
written  the  fire  in  the  Capitol  occurred,  and  in  order  to  ])reserve  the 
whispering  gallery,  whicii  jiad  l)ecome  an  object  of  unfailing  interest 
to  visitors  to  the  Capitol,  the  new  ceiling  was  made  "to  conform 
within  a  fraction  of  an  inch  "  to  the  dimensions  of  the  ceiling  which 
it  replaced.  Notwithstanding  this  care,  the  (piality  of  lh«>  room 
which  liad  long  made  it  the  best  and  the  best  known  of  whispering 
galleries  was  in  large  measure  lost.  Since  then  this  occurrence  has 
been  frequently  cited  as  another  of  the  mysteries  of  architectural 
acoustics  and  a  disproof  of  the  ])ossii»ilities  of  predicting  such  jjlie- 
nomena.  As  a  matter  of  fact,  it  was  exactly  the  reverse.  Only  the  part 
betwei-n  the  panels  was  reproduced  jn  the  original  dimensions  of  tlie 
dome.  The  ceiling  was  no  longer  sukioIIi,  Die  slalT  was  j)aiiell«-d  in 
real  recess  and  nliif,  and  the  result  but  confirmed  tiie  statement 
recorded  nearly  two  years  before  ii\  the  Dirlionuri/  of  Arcliileriiire. 

The  loss  of  this  fine  whispering  gallery  has  at  least  some  compen- 
sation in  giving  a  convincing  illustration,  not  merely  of  the  condi- 


260  WHISPERING  GALLERIES 

tions  which  make  towards  excellence  in  the  phenomenon,  but  also  of 
the  conditions  which  destroy  it.  The  effect  of  the  paneling  is  obvi- 
ous. Each  facet  on  the  complex  ceiling  is  the  source  of  a  wavelet  and 
as  these  facets  are  of  different  depths  the  resulting  wavelets  do  not 
conspire  to  form  the  single  focusing  wave  that  results  from  a  per- 
fectly smooth  dome.  In  a  measure  of  course  in  this  particular  case 
the  wavelets  do  conspire,  for  the  reflecting  surfaces  are  systeinati- 
cally  placed  and  at  one  or  the  other  of  two  or  three  depths.  The  dis- 
l)ersion  of  the  sound,  and  the  destruction  of  the  whispering  gallery  is, 
therefore,  not  complete. 

An  instructive  parallel  may  be  drawn  between  acoustical  and 
optical  mirrors : 

Almost  any  wall-surface  is  a  much  more  perfect  reflector  of 
sound  than  the  most  perfect  silver  mirror  is  to  light.  In  the  former 
case,  the  reflection  is  over  96  per  cent,  in  the  latter  case  rarely 
over  90. 

On  the  surfaces  of  the  two  mirrors  scratches  to  produce  equally 
injurious  effects  must  be  comparable  in  their  dimensions  to  the 
lengths  of  the  weaves  reflected.  Audible  sounds  have  wave  lengths 
of  from  half  an  inch  to  sixty  feet;  visible  light  of  from  one  forty- 
thousandth  to  one  eighty-thousandth  of  an  inch.  Therefore  while 
an  optical  mirror  can  be  scratched  to  the  complete  diffusion  of  the 
reflected  light  by  irregularities  of  microscopical  dimensions,  an 
acoustical  mirror  to  be  correspondingly  scratched  must  be  broken 
by  irregularities  of  the  dimensions  of  deep  coffers,  of  panels,  of 
engaged  columns  or  of  pilasters. 

Moreover,  just  as  remarkable  optical  phenomena  are  produced 
when  the  scratches  on  a  mirror  are  parallel,  equal,  equal  spaced,  or  of 
equal  depth,  as  in  mother  of  pearl,  certain  bird  feathers,  and  in  the 
optical  grating,  so  also  are  remarkable  acoustical  phenomena  pro- 
duced when,  as  is  usually  the  case  in  architectural  construction,  the 
relief  and  recess  are  equal,  equally  spaced,  or  of  equal  depth.  The 
panels  in  the  dome  of  the  Hall  of  Statues  of  course  diminish  to- 
ward the  apex  of  the  dome  and  are  thus  neither  equal  nor  equally 
spaced,  but  horizontally  they  are  and  produce  corresponding  phe- 
nomena. The  full  details  of  these  efiFects  are  a  matter  of  common 
knowledge  in  Physics  but  are  not  within  the  scope  of  the  present 


WHISPERING  GALLERIES  261 

discussion.  It  is  sufficient  to  say  that  the  general  result  is  a  disper- 
sion or  a  distortion  in  the  form  of  the  focus  and  that  the  general 
eflFect  is  to  greatly  reduce  the  efficiency  of  the  whispering  gallery, 
but  to  by  no  means  wholly  destroy  it,  as  would  be  the  case  with 
complete  irregularity. 

By  the  term  whispering  gallery  is  usually  understood  a  room, 
either  artificial  or  natural,  so  shaped  that  taint  sounds  can  be  heard 
across  extraordinary  distances.    For  this  the  Hall  of  Statues  was  ill- 
adapted,  partly  because  of  a  number  of  minor  circumstances,  but 
primarily  because  a  spherical  surface  is  accurately  adapted  only  to 
return  the  sound  directly  upon  itself.   When  the  two  points  between 
which  the  whisper  is  to  be  conveyed  are  separated,  the  correct  form 
of  reflecting  surface  is  an  ellipsoid  having  tlie  two  points  as  foci. 
When  the  two  points  are  near  together,  the  ellijisoid  resembles  more 
and  more  a  sphere,  and  the  latter  may  be  regarded  as  the  limiting 
case  when  the  two  points  coincide.    On  the  otlicr  liaiid.  wluii  tlie 
two  foci  are  very  far  apart  the  available  part  of  the  ellipsoid  near  one 
of  the  foci  resembles  more  and  more  a  paraboloid,  and  this  nuiy  be 
regarded  as  the  otlier  extreme  limiting  case  when  one  of  llie  foci  is  at 
an  infinite  or  very  great  distance.   I  know  of  no  building  a  consider- 
able portion  of  whose  wall  or  ceiling  surface  is  part  of  an  exact  ellip- 
soid of  revolution,  but  the  great  IMorniou  Tabernacle  in  Salt  Lake 
City  is  a  near  approximation.    Plans  of  this  remarkable  building  do 
not  exist,  for  it  was  laid  out  on  the  ground  without  the  aid  of  fonnal 
drawings  soon  after  the  settlers  had  completed  lluir  weary  pilgrim- 
age across  the  Utah  desert  and  settled  in  their  isolated  valley.   It  was 
built  without  nails,  which  were  not  to  be  had,  and  held  together 
merely  by  wooden  pins  and  tied  with  strips  of  buffalo  hide.    Not- 
withstanding this  construction,  and  notwithstanding  the  fact  Uiat  it 
spans  250  feet  in  length,  and  150  feet  in  breadth,  and  is  without  any 
interior  columns  of  any  .sort,  it  has  been  free  irom  the  necessity  of 
es.sential   rejjair  for  over  fifty  years.     As  the  photograph  (.Fig.  5) 
shows,  taken  at  the  time  of  building,  the  space  between  the  ceiling 
and  the  roof  is  a  wooden  bridge  truss  construction.     Tlioe  photo- 
graphs, given  by  the  elders  of  the  church,  are   themselves   inter- 
esting considering  the  circumsfances  uiuler  which  they  were  taken, 
the  early  dale  and  the  remote  location. 


1^^ 


l^l^'ni^T 


Fig.  i.     Exterior.  Mormon  Tabernacle,  Salt  Lake  City,  Utah. 


pK^^rrrrrg 


^-#^:^.:-^' 


Fig.  5.     Photograph  showing  CoustriKlinii.  Muriuoii  Tabernacle,  Salt  Lake  City,  Utah. 


□□ 


Fig.  6 


264  WHISPKHIXG  GALLERIES 

It  is  difficult  for  an  interior  photograph  of  a  smooth  ceiHng  to  give 
an  impression  of  its  shape.  An  idea  of  the  shape  of  the  interior  of  the 
Tabernacle  may  be  obtained,  liowever,  from  a  photograph  of  its  ex- 
terior. It  obviously  somewhat  resembles  an  ellipsoid  of  revolution. 
It  is  equally  obvious  that  it  is  not  exactly  that.  Nevertheless  there 
are  two  points  between  which  faint  soimds  are  carried  with  remark- 
able distinctness,  —  the  reader's  desk  and  the  front  of  the  balcony  in 
the  rear. 

The  essential  geometrical  property  of  an  ellipsoid  of  revolution  is 
that  lines  drawn  to  any  point  of  the  surface  from  the  two  foci  make 
equal  angles  with  the  surface.  It  follows  that  sound  diverging 
from  one  focus  will  be  reflected  toward  the  other.  The  preceding 
photographs  (Fig.  6)  show  the  progress  of  a  sound-wave  in  the 
model  of  an  idealized  whispering  gallery  of  this  type  in  which  the 
reflecting  surface  is  a  portion  of  a  true  ellipsoid  of  revolution. 

The  most  notable  whispering  gallery  of  this  type  is  that  described 
by  Sir  John  Herschel  in  one  of  the  early  scientific  encyclopedias,  the 
Encydo-pedia  Metropolitana  as  follows: 

In  the  Cathedral  of  Girgenti  in  Sicily,  the  slightest  whisper  is  borne  with 
perfect  distinctness  from  tlie  great  western  floor  to  tlie  cornice  behind  the 
higli  altar,  a  distance  of  250  feet.  By  a  most  unluckj'  coincidence  the  pre- 
cise focus  of  divergence  at  the  former  station  was  chosen  for  the  place  of  the 
confessional.  Secrets  never  intended  for  the  public  ear  thus  became  known, 
to  the  dismay  of  the  confessor  and  the  scandal  of  the  people,  by  the  resort 
of  the  curious  to  the  opposite  point,  which  seems  to  have  been  discovered 
by  accident 

Aside  from  the  great  distance  between  the  foci,  the  circumstances 
related  had  many  elements  of  improbability  and  the  final  discussion 
of  this  subject  was  postponed  from  year  to  year  in  the  hope  that  the 
summer's  work,  which  has  usually  been  devoted  to  the  study  of  Eu- 
ropean auditoriums,  would  carry  the  writer  near  Girgenti,  an  inter- 
esting but  rather  inaccessible  city  on  the  southwestern  coast  of 
Sicily.  Finally,  failing  any  especially  favorable  opportunity,  a  flying 
trip  was  made  from  the  north  of  Europe  with  the  study  of  this  gallery 
and  of  the  Ear  of  Dionysius  at  Syracuse  as  the  sole  objective.  On 
the  way  down  the  perplexity  of  the  case  was  increased  by  finding  in 
Baedeker  the  statement  that  there  is  a  noteworthy  whispering  gal- 


M 


Klii.   ;.       lilliTl'T.   (   allinlricl  •'(  (iiri^'liU.  >li  lis 


200  WinSPERIXG  GALLERIES 

lery  between  the  west  entrance  of  the  Cathedral  and  "the  steps  of 
tlie  liigh  altar."  Such  a  whisppnnf:r  fjallery  is  wholly  inconceivable. 
The  facts  showed  a  whispering  gallery  between  the  foci  as  described 
by  Herschel,  altliongh  the  accompanying  story  is  rendered  improb- 
able by  the  extreme  inaccessibility  of  the  more  remote  focus,  and  its 
very  conspicuous  jiosition.  Nor  is  the  distance  so  great  as  stated  l)y 
Herschel,  being  a  little  over  100  feet  instead  of  250  feet.  However, 
the  interest  in  this  whispering  gallery  arises  not  because  of  any  inci- 
dent attending  its  discovery,  but  because  it  illustrates,  albeit  rather 
crudely,  the  fonn  of  surface  giving  the  best  results  for  whispering 
between  two  very  widely  separated  points. 

As  already  stated  the  strictly  correct  form  of  surface  for  a  whisper- 
ing gallery  is  an  ellipsoid  of  revolution  whose  foci  coincide  with  the 
two  points  between  which  there  is  to  be  communication.  In  the 
whispering  gallery  in  the  Cathedral  of  Girgenti  (Fig.  7),  the  focusing 
surface  consists  of  a  quarter  of  a  sphere  prolonged  in  the  shape  of  a 
half  cylinder  fonning  the  ceiling  over  the  chancel.  This  is  obviously 
not  a  true  paraboloid,  and,  such  as  it  is,  it  is  interrupted  by  an  arch 
of  slight  reveal  where  the  cylinder  joins  the  sphere;  moreover,  the 
two  points  of  observation  do  not  lie  on  the  axis  of  revolution  as  they 
shovdd  for  the  best  result.  But  a  hemisphere  and  a  continuing  cylin- 
der make  a  fair  approach  to  a  portion  of  a  paraboloid;  and  while  the 
two  points  of  observation  are  not  on  the  axis  of  revolution,  they  are 
on  a  secondary  axis,  the  station  by  the  door  being  below,  and  the 
focus  in  the  chancel  being  at  a  corresponding  distance  above  the 
principal  axis. 

In  all  the  preceding  galleries,  there  is  but  a  single  reflection  be- 
tween the  radiant  and  the  receiving  foci.  There  are  others  in  which 
there  are  several  such  reflections.  \Yell-known  examples  are  the 
church  of  St.  John  Lateran  in  Rome  and  in  the  Salle  des  Cariatides 
in  the  Louvre. 

In  the  Church  of  St.  John  Lateran  (Fig.  8),  each  bay  in  the  great 
side  aisles  is  a  square  having  a  ceiling  which  is  approximately  a  por- 
tion of  a  sphere.  At  best,  the  approximation  of  the  ceiling  to  a  sphere 
is  not  close  and  the  ceiling  varies  from  bay  to  bay,  not  intentionally 
but  merely  as  a  matter  of  variation  in  construction.  In  one  bay  more 
closely  than  in  the  others  the  ceiling,  regarded  as  an  acoustical 


c 

5 


K 
3 


2(iS  AVHISPERIXG  GALLERIES 

mirror,  has  its  i'uci  Hourly  at  lioad  level.  In  consequence  of  this,  two 
obser^•ers  standing  at  opposite  corners  can  whisper  to  each  other 
with  liic  ceiling  as  a  reflecting  surface.  The  curvature  even  in  this 
bay  is  not  ideal  for  the  production  of  a  whisj)ering  gallery,  so  that 
thus  used  the  gallery  is  far  from  notable.  It  so  hai)pens,  however, 
that  the  great  square  columns  which  form  the  corners  of  each  bay 
have,  instead  of  sharp  corners,  a  reentering  cove  or  fluting  in  the  arc 
of  a  circle  and  over  twelve  inches  across  in  opening.  If  the  observers, 
instead  of  attempting  to  speak  directly  to  the  ceiling,  turn  back  to 
back  and  face  the  columns  standing  close  to  them,  this  great  fluting 
gathers  the  sound  from  the  speaker  and  directs  it  in  a  concentrated 
cone  to  the  ceiling;  this  returning  from  the  ceiling  to  the  opposite 
angle  of  the  bay  is  concentrated  by  the  opposite  fluting  on  the  other 
obser^'er.  In  more  scientific  language,  borrowed  from  the  nomencla- 
ture of  the  makers  of  optical  instruments,  the  flutings  increase  the 
angular  aperture  of  the  system. 

An  almost  exact  duplicate  of  this  whispering  gallery  is  to  be  found 
in  the  vestibule  of  the  Conservatoire  des  Arts  et  INIetiers  in  Paris. 
This  vestibule,  itself  also  an  exhibition  room  but  called  since  the  dis- 
covery of  its  peculiar  property  La  Salle-Echo,  is  square  with  rounded 
corners  and  a  low  domical  ceiling.  Here,  as  in  St.  John  Lateran,  the 
observers  face  the  corners  and  the  whisper  undergoes  three  reflec- 
tions between  the  foci.  The  fact  that  the  two  observers  are  back  to 
back  diminishes  the  sound  which  would  otherwise  pass  directly  be- 
tween them  and  makes  the  whispering  gallery  more  pronounced  and 
the  phenomenon  much  more  striking.  In  both  galleries  it  is  the  cus- 
tom for  the  observers  to  take  their  positions  in  a  somewhat  random 
numner.  The  correct  position  is  at  a  distance  from  the  concave 
cj'lindrical  surface  a  little  less  than  half  the  radius  of  curvature. 

In  these  whispering  galleries  the  surfaces  are  not  theoretically  cor- 
rect and  the  phenomenon  is  far  from  perfect.  This  failure  of  loud- 
ness and  distinctness  in  most  of  the  multiple  reflection  galleries  arises 
not  from  any  progressive  loss  in  the  many  reflections,  for  the  loss  of 
energy  in  reflection  is  practically  negligible.  Indeed,  given  ideally 
shaped  surfaces,  multiple  reflection  whispering  galleries  are  capable 
of  producing  exceptional  effect;  for  if  two  of  the  surfaces  be  very 
near  the  observers  they  may,  even  though  they  themselves  be  of 


Fio.  II,     Salic  <lc8  Curiatiilc*.  llic  I»uvrr,  I'arii. 


070  WHISPERING  GALLERIES 

small  clinu-nsions.  gather  into  the  phenomenon  very  large  portions  of 
the  emergent  and  of  the  fociLsed  whisper.  In  both  St.  John  Lateran 
and  La  Salle-Echo,  the  condensing  mirrors  are  cylindrical  and  gather 
the  sound  horizontally  only.  In  the  vertical  plane,  they  are  wholly 
without  effect. 

It  is  not  difficult  to  determine  the  correct  forms  for  the  extreme 
mirrors.  If  the  ceiling  be  flat,  the  reflecting  svu'faces  near  the  two 
observers  should  be  parabolic  with  the  axis  of  the  ]}araboloid  di- 
rected toward  the  center  of  the  ceiling,  the  correct  position  for  the 
mouth  of  the  s])eaker  and  the  ear  of  the  auditor  being  at  the  foci  of 
the  two  paraboloids.  If  the  ceiling  be  curved,  the  simplest  design  is 
when  the  first  and  last  reflector.s  are  portions  of  an  ellipsoid,  each 
with  one  focus  at  the  center  of  the  ceiling  and  the  other  at  one  of  the 
foci  of  the  system  as  a  whole.  Einally,  if  the  ceiling  be  curved,  there 
is  still  another  theoretical  shape  for  the  end  reflectors,  determined  by 
the  curvature  of  the  ceiling;  in  this  case  the  ideal  surface  is  not  a 
conic  surface,  nor  otherwise  geometrically  simple,  but  is  such  that  the 
converging  power  of  the  end  mirror  with  half  the  converging  power 
of  the  middle  mirror  will  give  a  plane  wave. 

It  is  obvious  that  the  accurate  fulfilling  of  these  conditions  by  acci- 
dent is  improbable,  but  they  are  at  least  api)roached  in  the  whisper- 
ing gallery  in  the  Salle  des  Cariatides  in  the  Louvre  (Fig.  9).  Along 
the  axis  of  the  room,  and  at  no  inconsiderable  distance  apart,  are  two 
large  shallow  antique  vases.  A  whisper  uttered  a  little  within  the  rim 
of  one  is  partially  focused  by  it,  is  still  further  focused  by  the  barrel- 
shaped  ceiling,  and  is  brought  to  a  final  focus  symmetrically  within 
the  rim  of  the  f lu-ther  vase.  It  is  evident  that  the  effect  is  dependent 
on  only  a  portion  of  each  vase,  but  this  portion  satisfies  the  necessary 
conditions  to  a  first  approximation  in  both  longitudinal  and  in  trans- 
verse section.  When  the  correct  foci  are  found  this  whispering  gallery 
is  very  distinct  in  its  enunciation.  It  would  be  even  more  distinct  if 
the  ceiling  of  the  room  were  slightly  lower,  or,  keeping  the  height  the 
same,  if  its  radius  of  curvature  were  slightly  greater.  It  would  be 
still  better  if  the  vases  were  slightly  deeper. 

The  whispering  gallery  which  has  received  the  greatest  amount  of 
discussion,  and  a  discussion  curiously  inadequate  in  view  of  the  emi- 
nence of  the  authorities  engaged,  is  the  circular  gallery  at  the  base  of 


Via.  10.     Section  ihrouRli  Doim-  ..f  St.  I'lmli.  Cntholnil.  I^.ml..n 


272  WHISPERING  GALLERIES 

the  dome  of  St.  Paul's  Cathedral  in  London.  This  gallery  was  first 
brought  into  scientific  consideration  by  Sir  John  Herschel,  who  in 
describing  it  stated  that  "tlie  faintest  sound  is  faithfully  conveyed 
from  one  sitle  to  the  other  of  the  dome,  but  is  not  heard  at  any  inter- 
mediate point."  According  to  Lord  Rayleigh,  whose  reference,  how- 
ever, I  am  unable  to  verify,  and  either  in  page  or  edition  must  be  in 
error,  an  early  explanation  of  this  was  by  Sir  George  Airy,  the  Astron- 
omer Royal,  who  "ascribed  it  to  the  reflection  from  the  surface  of  the 
dome  overhead."  Airy  coidd  have  been  led  into  such  error  only  by 
the  optical  illusion  whereby  a  dome  seen  from  within  seems  lower 
than  it  is  in  reality.  A  moment's  inspection  of  the  preceding 
illustration  (Fig.  10),  which  the  Clerk  of  the  Works  kindly  had  re- 
produced from  an  old  engraving  in  the  possession  of  the  cathedral, 
shows  that  this  explanation  would  be  incorrect.  The  guide  who  does 
the  whispering  usually  occupies  the  position  marked  "A";  the  other 
focus  is  in  the  position  marked  "  B."  The  focus  accounted  for  by  Airy 
would  be  high  up  in  the  dome.  Lord  Rayleigh  taking  exception  both 
to  the  statement  of  fact  by  Herschel  and  the  explanation  by  Airy 
wrote  "  I  am  disposed  to  think  that  the  principal  phenomenon  is  to  be 
explained  somewhat  differently.  The  abnormal  loudness  with  which 
a  whisper  is  heard  is  not  confined  to  the  position  diametrically  oppo- 
site to  that  occupied  by  the  whisperer,  and  therefore,  it  would  appear, 
does  not  depend  materially  upon  the  symmetry  of  the  dome.  The 
whisper  seems  to  creep  around  the  gallery  horizontally,  not  neces- 
sarily along  the  shorter  arc,  but  rather  along  that  arc  toward  which 
the  whisperer  faces.  This  is  in  consequence  of  the  very  unequal 
audibility  of  a  whisper  in  front  of  and  behind  the  speaker,  a  phe- 
nomenon which  may  easily  be  observed  in  the  open  air."  Lord 
Rayleigh's  explanation  of  the  phenomenon  in  this  case  as  due  to  the 
"cree{)ing"  of  the  sound  around  the  circular  wall  immediately  sur- 
rounding the  narrow  gallery  accessible  to  visitors  is  unquestionably 
correct.  It  is  but  another  way  of  phrasing  this  explanation  to  say 
that  the  intensification  of  the  sound  is  due  to  its  accumulation  when 
turned  on  itself  by  the  restraining  wall.  It  is  obvious  that  the  main 
intensification  arises  from  the  curved  wall  returning  on  itself.  Verti- 
cally, the  sound  spreads  almost  as  it  would  were  the  curved  wall 
developed  on  a  plane.    This  vertical  spreading  of  the  sound  is  in  a 


"WIITSPERIXG  GALLERIES  273 

measure  restricted  by  the  circular  floor  gallery  and  by  the  overhang- 
ing ledge  of  the  cornice  moulding.  The  cornice  can  be  made  to  con- 
tribute most  to  the  effect  by  nuiking  the  oirve  of  its  lines  below  the 
principal  jjrojecting  ledge,  liiat  which  corresponds  to  the  drij)  mould- 
ing of  an  exterior  cornice,  relatively  smooth  and  sinijjle. 

But  even  Lord  Rayleigh's  ex])lanation  does  not  fully  account  for 
the  truly  remarkable  (lualities  of  this  whispering  gallery,  'llu-re  are 
many  circular  walls  as  high,  as  hard,  and  as  snu)oth  as  that  in  St. 
Paul's  (iallery  but  in  which  the  whispering  gallery  is  not  to  be  com- 
pared in  quality.  The  rear  walls  of  many  semi-circular  auditoriiuns 
satisfy  these  conditions  without  jjroducing  jiarallel  results,  for  ex- 
ample in  the  Fogg  lecture-room  at  Harvard  I'niversity  l>efore  it  was 
altered,  and  in  the  auditorium  just  completed  at  Cornell  I'niversity. 
A  feature  of  the  whispering  gallery  in  St.  Paul's,  contributing  not  a 
little  to  its  efficiency,  is  the  inclination  of  its  wall,  less  noticeable  per- 
haps in  the  actual  gallery  than  in  the  architectural  "  Section."  The 
result  is  that  all  the  st)uiul  which  ])asses  the  (|uarter  point  of  the 
gallery,  the  ])oint  half  way  around  Ix-tween  the  foci,  is  brought  down 
to  tlie  le\('l  of  tlie  observer,  and,  ((iiiilniicd  with  the  reflection  from 
the  ledge  which  constitutes  the  broad  seat  running  entirely  around 
the  gallery,  confines  and  intensifies  the  sound.  This  feature  is  of 
course  of  unusual  occurrence. 

It  may  not  be  out  ot  iilace  to  give  the  dimensions  of  this  gallery. 
The  distance  from  focus  to  focus,  if  indeed  in  this  type  of  gallery 
they  can  be  called  foci,  is  1.50  feel.  The  wall  ha>  a  height  of  -2(1  feet, 
and  is  not  moulded  in  panels  as  shown  in  the  engraving,  i)ut  is  smooth 
except  for  eight  shallow  niches.  While  the  inclination  of  the  wall  in 
the  gallery  of  St.  Paul's  is  a  contributing  factor,  an  even  nu)re  etticient 
wall  would  have  been  one  very  slightly,  imleed  almost  impere«'i)tibly, 
curved,  the  section  being  the  arc  of  a  circle  struck  from  the  center  of 
the  dome  on  a  level  with  the  ob.servers.  Such  a  gallerj'  will  be  in  the 
dome  of  the  Missouri  State  ("apilol,  a  gallery  uni<|ue  in  this  respect 
that  it  will  have  been  planned  intentionally  by  the  architects.' 

A  discussion  of  noted  whimpering  galleries  would  not  l)e  nMuph-le 

'  The  liiiililiiiK  is  iii.w  (tmipl.l.-  t)m-  ..f  llir  anlill.-.  In.  Mr.  F:,1k<t1..ii  S««rl»..ul.  rriH.rl. 
that  tlie  wliisprriiig  galkr.v  in  tin-  .Inmr  .xiutly  fiillilU  I'n.f.-vvir  Sal.iiir'.  pn>lK-ti.>n.  ami 
liB.s  been  the  cause  of  much  curionity  nnd  n.iloiii.tlimcnt.  —  hxlitor. 


"274 


WIIISPERLXG  GALLERIES 


witlunil  iiK'iilioii  of  llio  famous  Ear  of  Dionysius  at  Syracuse.    A 
mile  out  from  the  present  city  of  Syracuse,  on  the  slope  of  the  terrace 

occupied  by  the  Neapolis  of 
the  ancient  city,  are  the  re- 
mains of  a  quarry  entered 
on  one  side  on  the  level  but 
cut  ])ack  to  perpendicular 
walls  from  a  hundred  to  a 
lumdred  and  thirty  feet  in 
lieight.  'J'his  old  ((uarry. 
now  overgrown  by  a  wild 
and  luxurious  vegetation,  is 
known  as  the  Latomia  del 
Paradiso.  At  its  western 
angle  is  a  great  grotto, 
shaped  somewhat  like  an 
open  letter  S,  210  feet  in 
winding  length,  74  feet  high, 
35  feet  in  width  at  the  base 
and  narrowing  rapidly  to- 
ward the  top.  The  inner- 
most end  of  this  grotto  is 
nearly  circular,  and  the 
rear  wall  slopes  forward  as 
it  rises  preserving  in  revolu- 
tion the  same  contour  that 
characterizes  the  two  sides 
throughout  their  length. 
The  top  is  a  narrow  channel 
of  a  uniform  height  and  but 
a  few  feet  in  width.  At  the 
innermost  end  of  this  chan- 
nel, at  the  apex  of  the  half 
cone  which  forms  the  inner 
end  of  the  grotto,  is  a  verti- 
cal opening  four  or  five  feet  square,  scarcely  visible,  certainly  not 
noticeable,  from  below.     This  opening  is  into  a  short  passageway 


Fig.  11.  Plan  and  Elevation,  with  Sectional 
Indication,  of  Ear  of  Dionysius,  Syracuse, 
Sicilv. 


Fig.  \i.    View  of  Oiitcr  0|icDing,  the  SoK-allorl  Kar  ut  Uionyiiui,  Syr»ru»r.  Sirilj . 


276  WHISPERIXG  GALLERIES 

which  k'ads  to  a  fliglit  of  steps  and  thence  to  the  ground  above  (Fig. 
11).  The  grotto  is  noted  for  two  somewhat  inconsistent  acoustical 
properties.  When  being  shown  tlie  grotto  from  below,  one's  atten- 
tion is  called  to  its  very  remarkable  reverberation.  When  above, 
one's  attention  is  called  to  the  ability  to  hear  what  is  said  at  any 
point  on  the  floor. 

It  is  related  that  Tyrant  Dionysius,  the  great  builder  of  Syracuse, 
so  designed  his  prisons  that  at  certain  concealed  points  of  observation 
he  could  not  merely  see  everything  that  was  done,  but,  through  re- 
markable acoustical  design,  could  hear  every  word  which  was  spoken, 
even  when  whispered  only  (Fig.  12).  There  is  a  tradition,  dating 
back  however  only  to  the  sixteenth  century,  that  this  grotto,  since 
then  called  the  Ear  of  Dionysius,  was  such  a  prison.  Quarries  were 
plausible  prisons  in  which  captives  of  war  might  have  been  com- 
pelled to  work,  and  there  are,  surrounding  this  quarry,  traces  of  a 
wall  and  sentry  houses,  but  there  is  no  direct  evidence  associating 
this  grotto  with  Dionysius,  unless  indeed  one  regards  its  interesting 
acoustical  properties  taken  in  connection  with  classical  tradition  as 
such  evidence. 

In  its  acoustical  property  this  grotto  resembles  more  a  great  ear 
trumpet  than  a  whispering  gallery  in  the  ordinary  sense  of  the  word. 
It  is,  of  course,  in  no  sense  a  focusing  whispering  gallery  of  the  type 
represented  by  the  vases  and  curved  ceiling  in  the  Louvre.  It  more 
nearly  resembles  the  gallery  in  St.  Paul's  Cathedral,  but  the  sound 
is  not  spoken  close  to  the  deflecting  wall,  one  of  the  essentially 
characteristic  conditions  of  a  true  whispering  gallery  of  that  type, 
and  tlie  wall  is  not  continuously  concave.  In  fact,  in  other  ways  also 
its  acoustical  property  is  not  very  notable,  for  distinctness  of  enun- 
ciation is  blurred  by  excessive  reverberation. 

It  is  conceivable  that  whispering  galleries  should  be  of  use  and 
purposeful,  but  it  is  more  probable  that  they  will  remain  architectural 
curiosities.  When  desired,  they  may  be  readily  woven  into  the  design 
of  many  types  of  monumental  buildings. 


APPENDIX 

NOTE  OX  MKASIHKMKNTS  Ol'  TlIK  INTFASITV  OF  SOIM)  WD 
ON    rilK  HKACTIO.N  OK   lliK  HOOM  ll'ON  THK  SOIM) 

Uiuixc  one  of  lluM';irlyl<'ctiin's  jjivi-n  at  the  Sorhoniu-  in  llu- spriiif,' 
of  1917,  rrotV.ssor  Sal)iiU'  n-frnvd  to  tlu>  diiiicullit-.s  iiilnTt-nt  in  t-x- 
pcriments  on  sound  intensities.  The  following;  is  a  free  translation 
from  I  lie  Holes,  in  French,  whiili  lie  iJiipand  for  tliis  lecture: 

In  no  other  donian  have  physicists  disregarded  the  conditions  in- 
troduced by  the  surrounding  materials,  hut  in  acoustics  these  do  not 
seem  to  have  received  the  least  attention.  If  measurements  are  made 
in  the  o])en  air,  over  a  lawn,  as  was  done  by  Lord  Rayleigh  in  Cfrlain 
experiments,  is  due  consideration  given  to  the  fact  that  the  surface 
has  an  absorbing  power  for  ^()Ull(l  of  from  40  to  00  percent?  Or,  if  in- 
side a  building,  as  in  Wieu's  similar  experiments,  is  allowance  made 
for  the  fact  that  the  walls  reflect  from  i):3  to  08  percent  of  the  souud? 
We  need  not  be  surprised  if  the  results  of  such  ex|)eriments  ditfer 
from  one  aiiollici'  l)y  ;i  fiicloi'  of  inorc  Ihaii  :i  liuiidred. 

II  would  i)c  no  nior<'  ali^urd  to  carrA'  out  photometric  nieasure- 
meuls  ill  a  room  where  the  wails,  ceiling,  and  even  the  floor  and  tables 
consisted  of  highly  polished  mirrors,  than  to  make  mea>uremeut>  on 
the  intensity,  or  on  the  (plant  it  at  ive  analysis  of  .sound,  under  the  con- 
ditions in  wliicli  sucli  e\|)eiiiiieiits  have  almost  iuvariaidy  been  exe- 
cuted. It  is  not  astonishing  that  we  have  been  discouraged  by  the 
results,  and  that  we  may  have  des])aire(l  of  seeing  acoustics  iH-cupy 
the  ijositioii  to  which  it  rightly  belongs  among  the  exact  .sciemvs. 

'I'lie  leiiglli  of  I  lie  Waves  of  ligiit  is  so  small  compared  with  the 
dimensions  of  a  photometer  I  liat  we  do  not  need  to  conn-rn  ourselves 
with  the  plieiiomeiia  of  interfercuee  while  measuring  the  intensity  of 
light.  In  the  case  of  sound,  however,  it  mu>t  be  (juite  a  dilTer»-nl 
matter. 

III  Older  to  show  lliis  ill  a  definite  manner.  I  have  niea.surv«l  tlie 
iuteiisily  of  the  sound  in  all  parts  of  a  certain  laboratory  nK.m.  For 
simplicity,  a  .symmetrical  room  was  .selecteil,  and  the  sount-,  giving  ii 
very  pure  tone,  was  placed  in  the  center.    It  was  fouiul  that,  near  tlu* 


'278  APPENDIX 

source,  oven  at  tlio  soiinr  itself,  the  intensity  was  in  reality  less  than 
at  a  distance  of  five  feel  from  the  source.  And  yet,  tJie  clever  experi- 
menter, Wien,  and  the  no  less  skillful  psychologists  Wundt  and 
Miinsterberg  have  Jissumed  under  similar  conditions  the  law  of  varia- 
tion of  intensity  with  the  inverse  square  of  the  distance.  It  makes 
one  wonder  how  they  were  able  to  draw  any  conclusions  from  their 
measurements. 

Not  only  do  the  walls  reflect  sound  in  such  a  way  that  it  becomes 
many  times  more  intense  than  it  otherwise  would  be;  and  not  only 
does  the  interference  of  soimd  exist  to  such  an  extent  that  we  find 
regions  of  maximum  and  regions  of  minimum  of  sound  in  a  room;  but 
even  the  total  quantity  of  sound  emitted  by  the  source  itself  may  be 
greatly  affected  by  its  position  with  regard  to  the  intierference  system 
of  the  room. 

This  will  be  more  readily  understood  if  illustrated  by  an  incident 
drawn  from  the  actual  experiments.  A  special  sort  of  felt,  of  strong 
absorbing  power,  was  brought  into  the  room  and  placed  on  the  floor. 
The  effect  was  two-fold.  First,  the  introduction  of  the  felt  increased 
the  absorption  of  the  sound,  and  thus  tended  to  diminish  the  total 
intensity  of  sound  in  the  room,  theoretically  to  a  third  of  its  previous 
value.  But  actually  it  had  the  contrary'  effect;  the  sound  became 
much  louder  than  before.  The  felt  was  so  placed  on  the  floor  as  to 
shift  the  interference  system  in  the  room,  and  thus  the  reaction  of  the 
sound  vibrations  in  the  room  upon  the  source  itself  was  modified. 
The  source  was  a  vibrating  diaphragm  situated  at  the  base  of  a  res- 
onating chamber.  In  its  first  location,  the  source  was  at  a  node  of 
condensation,  where  the  motion  of  the  sound  which  had  accumulated 
in  the  room  coincided  with  that  of  the  diaphragm.  It  was  thus  diffi- 
cult for  the  diaphragm  to  impart  any  additional  motion  to  the  air. 
In  the  second  case,  however,  the  vibrations  of  the  two  were  opposite; 
the  diaphragm  was  able  to  push  upon  the  air,  and  although  the  am- 
plitude of  its  motion  was  somewhat  reduced  by  the  reaction  of  the  air 
upon  it,  the  emitted  sound  was  louder.  When  under  these  conditions 
the  diaphragm  was  forced  to  vibrate  with  the  same  amplitude  as  at 
first,  the  emitted  sound  became  eight  times  louder. 

Naturally  these  two  positions  in  the  interference  system  were  de- 
signedly selected,  and  they  show  exceptional  reactions  on  the  source. 


AITFADIX  279 

However,  in  tlie  case  of  a  very  eoin|)lex  sound,  a  eoni]>araljle  iliver- 
gence  in  the  reaction  of  tlie  room  on  the  different  conipon<nt.s  of  tlie 
sound  would  be  probable. 

It  is  thus  necessary  in  quantitative  research  in  acoustics  to  take 
account  of  three  factors:  the  effect  of  reflection  by  the  walls  on  the 
increase  of  the  total  intensity  of  sound  in  the  room ;  the  effect  of  inter- 
ference in  greatly  altering  the  distribution  of  this  intensity;  and  the 
effect  of  the  reaction  of  the  sound  vibrations  in  a  room  upon  the 
source  itself.   .   .   . 

In  choosing  a  source  of  sound,  it  has  usually  been  assumed  that  a 
source  of  fixed  amplitude  was  also  a  source  of  fixed  intensity,  e.  g.,  a 
vibrating  diaphragm  or  a  tuning  fork  electrically  maintained.  ( )n  t  In- 
contrary,  this  is  just  the  sort  of  source  whose  emitting  power  varies 
with  the  ])osition  in  which  it  is  placed  in  tlie  room.  On  the  other 
hand,  an  organ  pipe  is  able  within  certain  limits  to  adjust  itself  auto- 
matically to  the  reaction  due  to  the  interference  system.  We  may 
say,  simj)ly,  that  the  best  standard  source  of  sound  is  one  in  which  the 
greatest  percentage  of  emitted  energy  takes  the  form  of  sound. 


PniXTED  AT 

THE  HARVARD  UXIVERSITV  PRESS 

CAMBRIDGE,  MASS.,  U.  S.  A. 


'NA2S00S121922 

HIIIIIIIIIIJIUIJI 

L  006  267  198  7 


D     000  580  671     6 


If 


i. 


